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simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. arrangements; finite Coxeter groups; finite complex reflection groups; decomposition classes; invariants; invariant polynomial functions; semisimple Lie algebras Douglass, J. Matthew; Röhrle, Gerhard, Invariants of reflection groups, arrangements, and normality of decomposition classes in Lie algebras, Compos. Math., 148, 3, 921-930, (2012) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. equivariant compactification; symmetric varieties; character sheaves; finite groups of Lie type | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Deligne-Lusztig varieties; finite groups of Lie type; Weyl groups; conjugacy classes; minimal length elements He, X., On the affineness of Deligne-Lusztig varieties, J. Algebra, 320, 3, 1207-1219, (2008) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. simple integrable modules; double affine Hecke algebras; perverse sheaves; linear algebraic groups; Lie algebras; Cartan subalgebras; Borel subalgebras; root systems; affine Weyl groups; simple reflections; pairings; equivariant \(K\)-theory; Jordan-Hölder multiplicities of induced modules Vasserot, Eric, Induced and simple modules of double affine Hecke algebras, Duke Math. J., 126, 2, 251-323, (2005) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. simple Lie algebras; McKay correspondence; Vogel's universality; Diophantine equations; regular maps Khudaverdian, H.M.; Mkrtchyan, R.L., Diophantine equations, platonic solids, mckay correspondence, equivelar maps and Vogel's universality, J. geom. phys., 114, 85-90, (2017) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Hilbert schemes of points; quiver varieties; HIrzebruch surfaces; ADHM data; monads; Nakajima quivers; McKay quivers; quiver varieties, moduli spaces of quiver representations Bartocci, C.; Bruzzo, U.; Lanza, V.; Rava, C.L.S., Hilbert schemes of points of \(\mathcal{O}_{\mathbb{P}^1}(- n)\) as quiver varieties, J. pure appl. algebra, 221, 2132-2155, (2017) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. word maps; finite groups of Lie type; equidistribution; trace polynomials Bandman, T.; Kunyavskii, B., Criteria for equidistribution of solutions of word equations on \(S L(2)\), J. Algebra, 382, 282-302, (2013) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. McKay correspondence; motivic integration; quotient singularities; finite group schemes | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. multiplicity; affine Kac-Moody Lie algebras; irreducible highest weight representations; theta functions; modular forms; Macdonald identities; string functions; generalized Kostant partition functions; identities for modular forms; elliptic theta functions Kač, VG; Peterson, DH, Infinite-dimensional Lie algebras, theta functions and modular forms, Adv. Math., 53, 125, (1984) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. McKay-type correspondence; Gorenstein singularities; modular invariants; orbifolds; super Yang-Mills theory Hanany, A.; He, Y-H, Non-abelian finite gauge theories, JHEP, 02, 013, (1999) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Hilbert schemes of points; symmetric functions; vertex algebras Lehn, M., Sorger, C.: Symmetric groups and the cup product on the cohomology of Hilbert schemes. Duke Math. J. \textbf{110}(2), 345-357 (2001). math/0009131 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Schur index; essential dimension; canonical dimension; representations of finite groups; Severi-Brauer varieties; central simple algebras | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Siegel modular forms; automorphic Borcherds products; theta functions and Jacobi forms; moduli space of abelian and Kummer surfaces; affine Lie algebras and hyperbolic Lie algebras | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. cross sections; Dynkin diagrams; idempotents; irreducible representations; \(\mathcal J\)-classes; \(({\mathcal J},\sigma)\)-irreducible monoids; lattices; multilined closures; one parameter closures; orbits; reductive groups; reductive monoids of Ree type; simple algebraic groups Li, Zhuo; Putcha, M., Types of reductive monoids, J. algebra, 221, 102-116, (1999) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. affine algebras; actions of finite dimensional cocommutative Hopf algebras; Noether's theorem; finite groups of automorphisms; triangular Hopf algebras; quantum-commutative modules; non-commutative determinant functions; symmetric braidings; twist maps; categories of modules; Grassmann algebras; group gradings Cohen, M.; Westreich, S.; Zhu, S., Determinants, integrality and Noether's theorem for quantum commutative algebras, Israel J. math., 96, 185-222, (1996) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. flag varieties; algebraic groups of type \(D_4\); triality; central simple algebras; orthogonal involutions; Clifford algebras Garibaldi, R. S.: Twisted flag varieties of trialitarian groups. Commun algebra 27, No. 2, 841-856 (1999) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Hilbert's fourteenth problem; algebraic group; finite; generation of algebra of invariant functions Grosshans, F.D.: Hilbert's fourteenth problem for non-reductive groups. Math. Z.193, 95--103 (1986) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. chip firing; toppling; sandpile; avalanche-finite matrix; Z-matrix; M-matrix; McKay correspondence; McKay quiver; root system; Dynkin diagram; minuscule weight; highest root; numbers game; abelianization | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. uniserial groups; infinitesimal groups; finite representation type; Witt vectors; Dieudonné modules; simple modules; group schemes Rolf Farnsteiner, Gerhard Röhrle, and Detlef Voigt, Infinitesimal unipotent group schemes of complexity 1, Colloq. Math. 89 (2001), no. 2, 179 -- 192. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. algebraic transformation groups; classification; convex geometry; geometry of algebraic groups; invariant theory; linear algebraic semigroups; linear algebraic monoids; linear semigroups; monoids of Lie type; normal algebraic monoids; Putcha lattices of cross-sections; reductive monoids; regular semigroups; Renner monoids; representation theory; spherical embeddings; strongly \(\pi\)-regular semigroups; Tits systems; torus embeddings Renner, L. E.: Linear algebraic monoids, Encyclopædia math. Sci. 134 (2005) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Hecke category; finite groups of Lie type; character sheaves; endoscopic group | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. \(E_8\); exceptional phenomena; Clifford algebras; icosahedral symmetry; Coxeter groups; root systems; spinors; Coxeter plane; Lie algebras; Lie groups; representation theory; quantum algebras; trinities; McKay correspondence | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. blocks; conjugacy classes; extension principle; finite monoids of Lie type; irreducible representations; linear algebraic monoids; modular representations; Morita equivalences; normal reductive monoids; Putcha lattices of cross-sections; representation theory; semisimple elements; solvable algebraic monoids Renner, L. E.: Representations and blocks of algebraic monoids, Fields inst. Commun. 40 (2004) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. rings of finite CM type; finitely many indecomposable Cohen-Macaulay modules; simple hypersurface singularities; scrolls; fixed rings; almost split sequences Auslander, M., Reiten, I.: The Cohen--Macaulay type of Cohen--Macaulay rings. Adv. Math. 73(1), 1--23 (1989) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. representations of quivers; invariant theory of classical groups; Luna slice theorem; representation spaces; supermixed quivers; dimension vectors; simple supermixed representations Bocklandt, R., A slice theorem for quivers with an involution, J. algebra appl., 9, 3, 339-363, (2010) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. irreducible characters; finite groups of Lie type; connected reductive group; Frobenius map; maximal torus; Borel subgroup; Deligne-Lusztig virtual characters; \(\ell \)-adic cohomology; semisimple classes; Jordan decomposition; irreducible constituents | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. infinitesimally faithful representations; reductive complex connected algebraic groups; Lie algebras; representation spaces; fields of rational functions; Cayley transforms; coordinate rings; regular orbits; varieties of unipotent elements Kostant, B.; Michor, P.; Christian, Duval, The generalized Cayley map from an algebraic group to its Lie algebra, \textit{Prog. Math.}, 213, 259-296, (2003), Birkhäuser, Boston, MA | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. K3 surfaces and Enriques surfaces; Lattices and Convex bodies; Simple groups and groups of Lie type; simple groups of Lie type; simple groups: sporadic groups Keum J.H., Oguiso K., Zhang D.-Q.: The alternating group of degree 6 in the geometry of the Leech lattice and K3 surfaces. Proc. Lond. Math. Soc. (3) 90(2), 371--394 (2005) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. group action; \(K\)-theory; derived category; quotient variety; resolution of singularity; motivic integration; McKay correspondence; Hilbert schemes of \(G\)-orbits; crepant resolution; discrepancy divisor; Klein quotient singularity Reid, Miles, La correspondance de McKay, Astérisque, 276, 53-72, (2002) | 1 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. matrix factorizations; triangulated categories; representations of Dynkin quivers; \(ADE\) singularities; Landau-Ginzburg orbifolds; mirror symmetries; path algebras; quiver representations; Auslander-Reiten quivers Kajiura, H.; Saito, K.; Takahashi, A., Matrix factorization and representations of quivers. II. type \textit{ADE} case, Adv. Math., 211, 1, 327-362, (2007) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. simple algebraic groups; generators; subring of invariants; ring of polynomial functions; adjoint representation; traces; generic matrices; good filtrations; direct summands; invariant polynomials; Poincaré series; ring of invariants Zubkov, AN, \textit{on the procedure of calculation of the invariants of an adjoint action of classical groups}, Comm. Algebra, 22, 4457-4474, (1994) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. semisimple, simply connected algebraic group; group scheme; maximal torus; character group; dominant weights; Coxeter number; G-module; group of rational points; injective hull; projective cover; affine Weyl group; fundamental dominant weights; Cartan invariants; composition factors; finite groups of Lie type Humphreys, J. E.: Generic Cartan invariants for Frobenius kernels and Chevalley groups. J. algebra 122, 345-352 (1989) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. central extensions of Lie algebras; conformal groups; Witt algebra; conformal field theories; central extensions of groups; two-dimensional conformal field theory; Virasoro algebra; conformal symmetries in dimension two; representation; Verma modules; Kac determinant; diffeomorphism group of the circle; bosonic string theory; Verlinde formula; fusion rule; dimension formula; spaces of generalized theta functions; moduli spaces of vector bundles; compact Riemann surfaces; bibliography Schottenloher, M.: A mathematical introduction to conformal field theory. (1997) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. inverse problem of Galois theory; Fischer-Griess monster as Galois group over \({\mathbb{Q}}\); finite simple groups; fundamental group; rigid simple groups; cyclotomic field; discrete subgroups of \(PSL_ 2({\mathbb{R}})\); congruence subgroup; modular curve; Puiseux-series; group of covering transformations; compact Riemann surface; algebraic function field; ramification points; cusps; lectures | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. representations of group schemes; representations of groups; Lie algebras; Auslander-Reiten sequences DOI: 10.1023/A:1009968402535 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Brauer-Severi schemes; matrix invariants; moduli spaces of representations of quivers; fibers; orders in central simple algebras; projective fiber bundles; trace rings of generic matrices L. Le Bruyn and G. Seelinger, Fibers of generic Brauer--Severi schemes, J. Algebra, 214 (1999), 222--234.Zbl 0932.16025 MR 1684876 and Applied Mathematics, 290, Chapman and Hall, 2008.Zbl 1131.14006 MR 2356702 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite-dimensional complex matrix Lie supergroups; affine group superschemes; Hopf algebras of polynomial functions; real forms; Heisenberg supergroups; matrix realizations H. Boseck, Classical Lie supergroups, Math. Nachr. 148 (1990), 81--115. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. complex multiplication; reciprocity laws for special values of Hilbert modular functions; arithmetic groups; Eisenstein series; maximal arithmetic groups; maximality of discrete groups of holomorphic automorphisms; adèle group; holomorphic modular forms Baily W L Jr, On the theory of Hilbert modular functions I, Arithmetic groups and Eisenstein series,J. Algebra 90 (1984) 567--605 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite dimensional modules; finitely generated algebras; Gabriel quivers; indecomposable Auslander-Reiten quivers; degenerations of modules; quiver representations; Grothendieck groups; affine varieties A. Skowronski and G. Zwara, ?Degenerations in module varieties with finitely many orbits,? Contemporary Mathematics 229 (1998), 343-356. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. monodromy groups of isolated singularities of hypersurfaces; free generators; free group; transformations; Dynkin diagram S. P. Humphries, ''On weakly distinguished bases and free generating sets of free group,''Quart. J. Math.,2, No. 36, 215--219 (1985). | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. inverse problem of Galois theory; Fischer-Griess monster as Galois group over \(\mathbb{Q}\); finite simple groups; fundamental group; rigid simple groups; cyclotomic field; discrete subgroups of \(PSL_2(\mathbb{R})\); congruence subgroup; modular curve; Puiseux series; group of covering transformations; compact Riemann surface; algebraic function field; ramification points; cusps J. Thompson , Some finite groups which appear as Gal (L/K) where K \subset Q(\mu n) , J. Alg. 89 (1984) 437-499. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. modular invariant theory; polynomial invariants; representations of finite groups; group action Campbell, H.E.A., Wehlau, D.L.: Modular Invariant Theory. Encyclopaedia of Mathematical Sciences, vol. 139. Springer, New York (2011) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. differential graded categories; triangulated categories; derived noncommutative schemes; finite-dimensional algebras; geometric realizations; noncommutative algebraic geometry; quasi-coherent sheaves; homological algebra; perfect complexes; unbounded derived category; enough injectives; classical generator; homotopy category; enhanced category; noncommutative scheme; noncommutative derived scheme; compactification; resolution of singularities; Serre functor; geometric realization; pure geometric realization; phantoms; quasi-phantoms; Krull-Schmidt partners | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. resolution of singularities; simple normal crossings; semisimple normal crossings; desingularization invariant; Hilbert-Samuel function; singularities of pairs; log-resolution of singularities Bierstone, Edward; Vera Pacheco, Franklin, Resolution of singularities of pairs preserving semi-simple normal crossings, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matematicas. RACSAM, 107, 159-188, (2013) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. algebraic geometry; zeta functions; L-functions; schemes of finite type; analytic continuation; rationality; Artin-Chebotarev density theorem . J-P. Serre, ''Zeta and \(L\) functions,'' in Arithmetical Algebraic Geometry, New York: Harper & Row, 1965, pp. 82-92. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. representation theory; reductive algebraic groups; simple G-modules; highest weights; character formula; Weyl's formula; affine group schemes; injective modules; injective resolutions; derived functors; Hochschild cohomology groups; hyperalgebra; split reductive group schemes; Steinberg's tensor product theorem; irreducible representations; Kempf's vanishing theorem; Borel-Bott-Weil theorem; characters; linkage principle; dominant weights; filtrations; Steinberg modules; cohomology ring; ring of regular functions; Schubert schemes; line bundles [6] Jantzen J.\ C., Representations of Algebraic Groups, Academic Press, Orlando, 1987 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. ring of invariants; reduced Grothendieck group; simple hypersurface singularities; stable AR-quivers; exponential-type operators; uniform approximation Jürgen Herzog and Herbert Sanders, The Grothendieck group of invariant rings and of simple hypersurface singularities, Singularities, representation of algebras, and vector bundles (Lambrecht, 1985) Lecture Notes in Math., vol. 1273, Springer, Berlin, 1987, pp. 134 -- 149. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. resolution of singularities; stable simple normal crosssings; desingularization invariant; Hilbert-Samuel function; presentations | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. irreducible representations; group schemes; Lie algebras of Cartan type; injective representations DOI: 10.1080/00927879608825553 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. type vector; finite set of points in \(\mathbb{P}^n\); Hilbert functions; \(k\)-configurations; arrangements; number of minimal generators; lex-segment ideal; maximal graded Betti numbers; liaison Geramita, A. V.; Harima, T.; Shin, Y. S.: Extremal point sets and Gorenstein ideals. Queen's papers in pure and appl. Math. 114, 99-140 (1998) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. ADE singularities; hypersurface singularities of finite deformation type; hypersurface singularities with finite Cohen-Macaulay type; normal forms for simple singularities Greuel, G.-M., Kröning, H.: Simple singularities in positive characteristic. Math. Z. 203(2), 339-354 (1990). Zbl 0715.14001 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. regular modules; stretched modules; tame concealed algebras; tame quivers; indecomposable quivers; simple quivers; path algebras; finite dimensional modules; finite dimensional associative algebras; cancellation theorems; degenerations of modules; preprojective modules; modules over tame concealed algebras; matrix pencils Bongartz, K., On degenerations and extensions of finite dimensional modules, \textit{Adv. Math.}, 121, 245-287, (1996) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. variation of complex structures; variation of Lie algebras; simple-elliptic singularities; 1-parameter families Seeley C, Yau Stephen S-T. Variation of complex structures and variation of Lie algebras. Invent Math, 1990, 99: 545--566 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. multiplicity of reflection representation; arrangements of hyperplanes; finite Coxeter groups; Weyl groups; Springer representations; classical groups; Lie algebras; connected reductive algebraic groups; Borel subgroups; \(l\)-adic cohomology; cohomology groups; parabolic subgroups N. Spaltenstein, On the reflection representation in Springer's theory, Comment. Math. Helv. 66 (1991), no. 4, 618--636. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite-dimensional algebras; moduli spaces; simple modules; Grassmannians; projective varieties; quivers; finite local representation type; degenerations B. Huisgen-Zimmermann, ''Classifying representations by way of Grassmannians,'' Trans. Am. Math. Soc., 359, 2687--2719 (2007). | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. semisimple complex Lie groups; invariant theory; skew multiplicity-free actions; supersymmetric algebras; finite-dimensional representations; skew multiplicity-free representations; exterior algebras | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. semi-invariants of quivers; semi-invariant polynomial functions; affine varieties of quivers; complete intersections; tame algebras; Auslander-Reiten quivers Bobiński, G.; Riedtmann, Ch.; Skowroński, A.: Semi-invariants of quivers and their zero sets, EMS ser. Congr. rep., 49-99 (2008) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. central simple algebras; involution of orthogonal type; \(\sigma\)- symmetric elements; reduced norm; similitudes; quaternion algebras; discriminant extensions; Clifford algebras; algebras with involution; Clifford bimodules; Clifford groups; homogeneous varieties; semisimple linear algebraic groups; Brauer groups Merkurjev, A.; Tignol, J., The multipliers of similitudes and the Brauer group of homogeneous varieties, Journal für die Reine und Angewandte Mathematik, 461, 13-47, (1995) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. complex analytic groups; complex Hopf algebras of representative functions; complex algebraic group; analytic embeddings; semi-direct product; maximal reductive subgroup; normal reduced split hull; semi- simple representations | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Morita matrix rings; commutative MM rings; full matrix rings; finitely-generated projective modules; polynomial identities; von Neumann regular algebras; rings of formal power series; partial quotient rings; Picard groups; ideal class groups P. Merisi and P. Vámos, On rings whose Morita class is represented by matrix rings , J. Pure Appl. Alg. 126 (1998), 297-315. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite groups; invariant algebras; finite linear groups; actions; reductive groups; geometric theory of invariants; oblique reflections V. F. Ignatenko, ''Invariants of finite and infinite groups generated by reflections,''J. Math. Sci.,76, No. 3, 334--361 (1996). | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. fundamental groups; modular varieties; Galois groups; motives; Lie algebras; complexes; polylogarithms; cohomology of arithmetic groups Goncharov, AB, The dihedral Lie algebras and Galois symmetries of \( \uppi_1^{(1)}\left( {{{\text{P}}^1}-\left( {\left\{ {0,\infty } \right\}\cup {\mu_{\text{N}}}} \right)} \right) \), Duke Math. J., 110, 397, (2001) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. generalized quiver representations; classical groups; quivers with involution; Dynkin graphs; tame representation type; orthogonal groups; symplectic groups; reductive algebraic groups; general linear groups; finite representation type Derksen, H., Weyman, J.: Generalized quivers associated to reductive groups. Colloq. Math. 94(2), 151--173 (2002) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Lie algebras; orbits; spin; Chevalley generators; Capelli identity; forms; invariants; omega process; differential operators; generating systems; invariant theory; polarization process; general linear groups; classical groups; representation theory; dual pairs; enveloping algebras; algebras of invariant differential operators; actions; highest weights; quantum groups Umeda, T.: The capelli identities, a century after Sūgaku. 46, 206-227 (1994) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. affine Lie algebras; resolutions of simple surface singularities | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. symmetry; invariant; regular element; Platonic solids; binary polyhedral groups; Kleinian singularities; simply laced Lie algebras | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. algebraic groups; category of rational modules; projective modules; affine group schemes; cocommutative Hopf algebras; category of modules; dual Hopf algebras; category of locally finite modules; enveloping algebras; group algebras Donkin, S, On projective modules for algebraic groups, J. Lond. Math. Soc. (2), 54, 75-88, (1996) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. connected simply connected simple algebraic \(\mathbb{Q}\)-groups; smooth affine group schemes of finite type; special fibres; \(\mathbb{Q}\)-groups admitting \(\mathbb{Z}\)-models; Euler-Poincaré characteristic; mass formula; adjoint representations B.H. Gross, Groups over \(\(\mathbb {Z}\)\). Invent. Math. 124(1-3), 263-279 (1996) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. adjoint quotient; stratified Kähler space; Poisson manifold; Poisson algebra; Poisson cohomology; holomorphic quantization; reduction and quantization; geometric quantization; quantization on a space with singularities; normal complex analytic space; locally semialgebraic space; constrained system; invariant theory; bisymmetric functions; multisymmetric functions; quantization in the presence of singularities; costratified Hilbert space Huebschmann, J.: Stratified Kähler structures on adjoint quotients | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. toric varieties; freeness of cohomology groups; McKay correspondence; three-dimensional abelian quotient singularities | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. rational Cherednik algebras; category \(\mathcal O\); Hilbert schemes of points; complex semisimple Lie algebras Raphaël Rouquier, Representations of rational Cherednik algebras, Infinite-dimensional aspects of representation theory and applications, Contemp. Math., vol. 392, Amer. Math. Soc., Providence, RI, 2005, pp. 103 -- 131. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. semisimple complex Lie groups; invariant theory; skew multiplicity-free actions; supersymmetric algebras; finite-dimensional representations; skew multiplicity-free representations; exterior algebras | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. character varieties; quiver representations; Hilbert schemes; representations of finite general linear groups Hausel, Tamás and Letellier, Emmanuel and Rodriguez Villegas, Fernando, Arithmetic harmonic analysis on character and quiver varieties~{II}, Advances in Mathematics, 234, 85-128, (2013) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Kleinian singularities; representations of McKay quivers; linear modification; invariant theory | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite dimensional algebras; representations; degenerations of modules; Auslander-Reiten quivers; Dynkin quivers; indecomposable modules; tilted algebras; exact sequences Zwara, G, A degeneration-like order for modules, Arch. Math., 71, 437-444, (1998) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. categories of finite dimensional modules; hereditary categories of coherent sheaves; canonical algebras; path-algebras; quivers; tame concealed algebras; extended Dynkin diagrams; tubular algebras; wild quivers; Auslander-Reiten quivers; separating families; orthogonal standard tubes; preprojective components; indecomposable projectives; Auslander-Reiten components; quasitilted algebras; weighted projective lines; tilting vector bundles; minimal projective generators; right perpendicular categories; endomorphism rings; categories of finite length sheaves; relative Auslander-Reiten translations; wild tilted algebras; dimension vectors Lenzing, H.; de la Peña, J. A., Wild canonical algebras, Math. Z., 224, 403-425, (1997) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. semi-invariants of quivers; complete intersections; representations of quivers; prehomogeneous dimension vectors; algebras of semi-invariant functions Christine Riedtmann and Grzegorz Zwara, On the zero set of semi-invariants for quivers, Ann. Sci. École Norm. Sup. (4) 36 (2003), no. 6, 969 -- 976 (2004) (English, with English and French summaries). | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite groups generated by reflections; invariant differential forms; rings of invariant polynomials; exterior algebras A. Shepler, ''Semi-invariants of finite reflection groups,'' J. Algebra 220 (1999), 314--326. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. artinian algebras; thick points; noncommutative deformations; deformation functor; versal deformation; moduli suite; extensions; simple modules; phase space functor; Hochschild cohomology; Massey products; representations of associative algebras; Toy model; blow-ups; desingularizations, Hilbert schemes; Chern classes, Dirac derivation, de Rham complex; Jacobian conjecture; dynamical structure; swarms; metrics, gravitation; quantum gravitation; energy; Clifford algebras; Chern-Simons classes; Yang-Mills theory; heat equation; thermodynamics; Kepler laws; heat equation; Navier-Stokes equation; Schrödinger equation; Einstein field equation; entropy; cosmology; cosmological time; density of mass; inflation; cyclical cosmology; conformally trivial cosmological model; universe, observers; photons; red-shift; entanglement; consciousness; super symmetry bosonic fields; fermionic fields; gluons; quarks; charge; black energy; black mass | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. semisimple simply connected algebraic groups; Lie algebras; fields of formal Laurent series; Iwahori subgroups; Iwahori subalgebras; finite dimensional projective varieties; dimensions; explicit formula R. Bezrukavnikov, ''The dimension of the fixed point set on affine flag manifolds,'' Math. Res. Lett., vol. 3, iss. 2, pp. 185-189, 1996. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. almost versal families of modules; finite representation type; finite dimensional algebras; Cohen-Macaulay rings of Krull dimension 1; non-commutative Cohen-Macaulay algebras; projective varieties; tame algebras; curve singularities Drozd, Yu. and Greuel, G.-M.: Semi-continuity for Cohen--Macaulay modules, Math. Ann. 306 (1996), 371--389. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. central simple algebras; Brauer groups; adjoint semisimple linear algebraic groups; Borel varieties; twisted flag varieties; projective varieties; change of Schur index; function fields; groups of inner type; parabolic subgroups; index reduction formula; Brauer-Severi varieties A. S. Merkurjev, I. A. Panin, A. R. Wadsworth, \textit{Index reduction formulas for twisted flag varieties}. I, \(K\)-Theory \textbf{10} (1996), no. 6, 517-596. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Deligne-Lusztig varieties; finite groups of Lie type; Weyl groups; conjugacy classes Bonnafé, C.; Rouquier, R., Affineness of Deligne-Lusztig varieties for minimal length elements, J. Algebra, 320, 3, 1200-1206, (2008) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. loop groups; representations of quantum affine algebras; quantum groups at roots of 1; Riemann-Hilbert factorization; Poisson-Lie groups; \(G\)-bundles on an elliptic curve | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. polarizations; nullcones; qubits; Hilbert-Mumford criterion; finite-dimensional modules; complex reductive groups; homogeneous invariant functions; coordinate rings Hanspeter Kraft and Nolan R. Wallach, Polarizations and nullcone of representations of reductive groups, Symmetry and spaces, Progr. Math., vol. 278, Birkhäuser Boston, Inc., Boston, MA, 2010, pp. 153 -- 167. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Hilbert schemes of points on a surface; quasi-modular forms; multiple zeta value; generalized partition | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. prehomogeneous vector spaces of commutative parabolic type; prehomogeneous vector spaces of parabolic type; functional equations; zeta functions; parabolic subalgebras; semisimple Lie algebras Rubenthaler H., Algèbres de Lie et Espaces Préhomogènes (1992) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. representations of quivers; quiver coefficients; Grothendieck classes; Young diagram; Dynkin type Buch, A.S., Quiver coefficients of Dynkin type, Mich. Math. J., 57, 93-120, (2008) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. group of diagonal matrices; G-invariant regular functions; differential operators; G-stable Lie subalgebra; enveloping algebra; simple quotient; generalized Verma module; primitive factor ring; rings of differential operators Musson, I. M.: Actions of tori on Weyl algebras. Comm. alg. 16, 139-148 (1988) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Hilbert schemes; orbifold Euler characteristics; irreducible components of exceptional set; superstring theory; McKay correspondence Ito, Y., Nakamura, I.: McKay correspondence and Hilbert schemes. Proc. Japan Acad. Ser. A Math. Sci., 72, 135--138 (1996) | 1 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. simple singularities; resolution of singularities; Lie algebras; subregular nilpotent elements Lê, D. T.; Tosun, M., Simple singularities and simple Lie algebras, \textit{TWMS J. Pure Appl. Math.}, 2, 1, 97-111, (2011) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Simple Lie algebras; finite order automorphisms; index of a representation W. de Graaf, O. Yakimova, Good index behaviour of {\(\theta\)}-representations, I, Algebr. Represent. Theory 15 (2012), no. 4, 613--638. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. infinite dimensional Hilbert manifolds; compact simple Lie group; smooth based loops; Kač-Moody groups; flag manifold; homogeneous Kähler metrics; curvature; representation theory; intrinsic geometry; first Chern class; dual Coxeter number; Fredholm structure; holonomy bundle; index theorem; families of Fredholm operators; affine Kač-Moody group; Kač character formula; instantons on the 4-sphere Freed, D.: Flag manifolds and infinite dimensional Kähler geometry. Infinite dimensional groups (1985) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. exceptional vector bundles; perpendicular categories; finite-dimensional hereditary algebras; simple modules; Grothendieck groups; Auslander-Reiten components; indecomposable injective objects; tilting sheaves; endomorphism rings; tame concealed quivers | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. categories of modules; generalized Beilinson algebras; group schemes; modules of constant Jordan type; \(W\)-modules; equal images property; modular representations Julia Worch, Categories of modules for elementary abelian \?-groups and generalized Beilinson algebras, J. Lond. Math. Soc. (2) 88 (2013), no. 3, 649 -- 668. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Dynkin quivers; tame quiver algebras; singularities of representations of quivers I. Wolters, On deformations of the direct sum of a regular and another indecomposable module over a tame quiver algebra, Dissertation Berg. Univ. Wuppertal, 2008, 151 pages, available from Internet: URN: urn:nbn:de:hbz:468-20090102. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. semisimple modules; Jacobson radical; central simple algebras; Brauer group; primitive rings; density theorem; representations of finite groups; global dimension; textbook Farb, B.; Dennis, R. K.: ''Noncommutative algebra,'', graduate texts in mathematics. (1993) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Hirzebruch genus; automorphic correction of elliptic genus; modified Witten genus; Jacobi form; Jacobi theta-series; logarithmic derivative; quasi-modular Eisenstein series; derivatives of Weierstrass \(\wp\)-function; complex manifolds; graded ring of weak Jacobi forms; Calabi-Yau manifolds; Lorentzian Kac-Moody Lie algebras of Borcherds type; elliptic genus V. Gritsenko, \textit{Complex vector bundles and Jacobi forms}, math/9906191 [INSPIRE]. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite generation of algebra of invariant functions; Hilbert's fourteenth problem; algebraic group Grosshans, F., \textit{hilbert's fourteenth problem for non-reductive groups}, Math. Z., 193, 95-103, (1986) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. quiver varieties; Dynkin quiver of finite type A; partial flag manifolds; convolution product; equivariant \(K\)-groups; cyclic quiver variety; quantized enveloping algebra; Kac-Moody algebra; toroidal algebras Varagnolo, M., Vasserot, E.: On the \(K\)-theory of the cyclic quiver variety. Int. Math. Res. Not. no. 18, 1005-1028 (1999). arXiv:math/9902091. http://dx.doi.org/10.1155/S1073792899000525 | 0 |
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