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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. smooth algebraic groups; blocks; representation types; Auslander-Reiten quivers; Frobenius kernels; distribution algebras; complexity; infinitesimal group schemes Farnsteiner, R.: Block representation type of Frobenius kernels of smooth groups. J. Reine Angew. Math. 586, 45--69 (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. Beauville form; Fujiki invariant; irreducible hyperkähler manifold; locally symmetric variety of orthogonal type; period domain; Torelli theorem; modular form; cusp form; Weyl group; Zagier L-function; Cohen number; Siegel's formula V. Gritsenko, K. Hulek and G.\ K. Sankaran, Moduli spaces of irreducible symplectic manifolds, Compos. Math. 146 (2010), no. 2, 404-434. | 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. motivic integration; orbit method; arithmetic lattices; irreducible complex representations; algebraic groups; congruence subgroup property; polynomial representation growth; irreducible complex characters; representation zeta functions; subgroups of finite index; local zeta functions N., Avni., Arithmetic groups have rational representation growth, Annals of Mathematics, 174, 1009-1056, (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. Toda type flow; flows of spinning top type; Lie algebra representation; theory of correspondences; linearization of Hamiltonian system; Jacobi varieties; representation theory; algebraic curve; Kac-Moody algebras M. Adler and P. van Moerbeke, ''Linearization of Hamiltonian systems, Jacobi varieties, and representation theory,'' Adv. Math.,38, No. 3, 318--379 (1980). | 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. moduli spaces; preprojective algebras; tilting theory; McKay correspondence; Kleinian singularities Sekiya, Y.; Yamaura, K., \textit{tilting theoretical approach to moduli spaces over preprojective algebras}, Algebr. Represent. Theory, 16, 1733-1786, (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. Godeaux surface; constructing surfaces of general type; configurations of singularities; Campedelli surface; fundamental groups Miles Reid, Campedelli versus Godeaux, Problems in the theory of surfaces and their classification (Cortona, 1988) Sympos. Math., XXXII, Academic Press, London, 1991, pp. 309 -- 365. | 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. plane curves; zeta function; Jacobian conjecture; Puiseux expansions; singularities; pencils of conics; universal schemes; Hilbert scheme I. R. Shafarevich, \textit{Basic Algebraic Geometry} (Nauka, Moscow, 1988; Springer, Berlin, 2013), Vol. 1. | 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. elliptic curves; algebraic curves; group schemes; modular functions; \(L\)-functions; theta functions; Fermat's last theorem; conjecture of Birch and Swinnerton-Dyer; Shimura-Taniyama-Weil conjecture; Calabi-Yau varieties; string theory; cryptography; Hopf algebroids; elliptic cohomology Husemöller, D.: Elliptic Curves. Graduate Texts in Mathematics, 2nd edn. Springer, Berlin (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. reductive groups; nilpotent orbits; completely reducible subgroups; principal homomorphisms; Springer isomorphisms; geometric invariant theory; optimal cocharacters; linear representations; weights; Lie algebras McNinch, G., Optimal \(S L(2)\)-homomorphisms, Comment. Math. Helv., 80, 2, 391-426, (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. smooth structures on elliptic surfaces with finite fundamental group; topological classification of four-manifolds with special fundamental groups; geometric genus; blow-ups; intersection form; signature; Euler characteristic; Kirby-Siebenmann invariant; fundamental class; manifolds with finite cyclic fundamental groups; algebraic surface with nontrivial finite cyclic fundamental group; distinct smooth structures Hambleton I., Kreck M.: Cancellation, Elliptic Surfaces and the Topology of Certain Four-Manifolds. J. Reine Angew. Math. 444, 79--100 (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. height function; Mordell's conjecture; twisted Fermat curves; dual pairs of type II; symplectic form; unitary groups; irreducible dual reductive pairs; parabolic subgroups; non-ramified type I dual reductive pairs; irreducible admissible representations; Hecke algebras DOI: 10.1112/plms/s3-55.3.465 | 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 subgroups of \(SL (3,\mathbb{C})\); quotient varieties; isolated singularities; ring of invariant polynomials S. Yau and Y. Yu, \textit{Gorenstein quotient singularities in dimension three}, \textit{Mem. Amer. Math. Soc.}\textbf{505}, American Mathematical Society, Providence RI U.S.A., (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. automorphic forms; Kac-Moody algebras; theta correspondence; theta functions; multiplicative correspondence; modular forms; meromorphic modular forms; K3 surfaces; mirror symmetry; string theory; Donaldson invariants Kontsevich, M., Product formulas for modular forms on O(2, n) (after R.borcherds), Astérisque, 245, 41, (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. theory of invariants; Hilbert series; finite generatedness; freeness; asymptotics; noncommutative invariant theory of \(SL(2,\mathbb{C})\) Almkvist, Gert: Commutative and noncommutative invariant theory, Banach center publ. 26, 259-268 (1990) | 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 ring; finite group; progenerators; commutative monoid; group of units; Schur group; Munn algebras; semigroup rings; finite completely 0- simple semigroups Sundhir, N. R.: On classification of semigroup rings. Semigroup forum 40, 159-179 (1990) | 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; unirationality of conic bundles; central simple algebra; rational splitting field | 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. motivic zeta function; motivic convolution; families of varieties; Grothendieck ring; \(n\)-jet spaces; motivic measures; stringy invariants of singularities; arc spaces; Thom-Sebastiani property; motivic McKay correspondence Looijenga, E., Motivic measures, Séminaire Bourbaki 874, Astérisque, 276, 267-297, (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. cusp singularity; group action; crepant resolution; McKay correspondence; Coxeter-Dynkin diagram; Gabrielov numbers | 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. sigma form of Painlevé VI; two-point correlation functions of the lattice Ising model; Fuchsian linear differential equations; complete elliptic integrals; elliptic representation of Painlevé VI; scaling limit of the Ising model; susceptibility of the Ising model; singular behaviour; Fuchsian linear differential equations; apparent singularities; Landau singularities; pinch singularities; modular forms; Landen transformation; isogenies of elliptic curves; complex multiplication; Heegner numbers; moduli space of curves; pointed curves S. Boukraa, S. Hassani, J.-M. Maillard, B. M. McCoy, W. P. Orrick, and N. Zenine, ``Holonomy of the Ising model form factors,'' Journal of Physics A, vol. 40, no. 1, pp. 75-111, 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. algebras of invariants; representation theory; finite reflection groups; graded polynomial 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. matrices over ring; conditional expectation; Positivstellensätze; sums of squares; noncommutative associative algebras; algebras with involutions; Ore condition; diagonalization; quivers; path algebra; cyclic algebra; enveloping algebra of Lie algebra; path algebras; crossed product algebras; matrix polynomials; preordering; Lie algebras; Weyl algebras Savchuk, Y; Schmüdgen, K, Positivstellensätze for algebras of matrices, Linear Algebra Appl., 43, 758-788, (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. perverse sheaves; graded Lie algebras; canonical bases; connected reductive algebraic groups; algorithms; multiplicities of local systems; intersection cohomology sheaves Lusztig, G, Graded Lie algebras and intersection cohomology, representation theory of algebraic groups and quantum groups, Progr. Math., 284, 191-244, (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. generating functions of Poincaré polynomials of moduli spaces; Lerch sum; theta function; conjecture by Vafa and Witten; mixed mock modular form; exact formula of Rademacher-type; Fourier coefficients Bringmann, K.; Manschot, J., From sheaves on \(\mathbb{P}^2\) to a generalization of the Rademacher expansion, A. J. Math., 135, 1039-1065, (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. hyper-Kähler manifolds; Hilbert schemes; finite group actions; sporadic groups; Moonshine | 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. degenerations of modules; representations of quivers; top-stable degenerations; finite-dimensional representations; finite-dimensional algebras; radical layerings; layer-stable degenerations -, Top-stable degenerations of finite dimensional representations I, posted at www.math.ucsb.edu/\( \sim \)birge/papers.html. | 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 singular connection of spectral type; moduli space of parabolic connections; symplectic structure; Riemann-Hilbert correspondence; geometric Painlevé property; isomonodromic deformation of linear connection; higher dimensional Painlevé equations | 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 modular threefolds; toroidal compactification; Eisenstein series; symmetric Hilbert modular varieties; canonical model; resolution of singularities; Hilbert modular forms; octic | 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. subalgebras of algebras of differential operators; smooth varieties; associated graded algebras; regular functions; cotangent bundle; filtrations; graded cofinite subalgebras; algebras of invariants; finite group actions doi:10.1307/mmj/1144437435 | 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. Gorenstein singularities; \(\mathbb Q\)-Gorenstein singularities; quasi-homogeneous surface singularities; higher spin structures; moduli spaces; Arf functions; lifts of Fuchsian groups | 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 functions; points in generic position; ideal of points; number of generators; Cohen-Macaulay type; minimal resolution conjecture; Betti numbers Lorenzini, A.: The Minimal Resolution Conjecture. J. Algebra156, 5--35 (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. essential dimension; essential \(2\)-dimension; central simple algebras; fields of definition; involutions; categories of field extensions; transcendence degrees; Brauer groups; cyclic algebras A. Vishik, \textit{Direct summands in the motives of quadrics}, preprint, 1999, available at http://www.maths.nott.ac.uk/personal/av/papers.html. | 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. holomorphic functions of several variables; algebraic geometry; complex semisimple Lie groups; abstract harmonic analysis; local rings and varieties; nullstellensatz; dimension; homological algebra; sheaf cohomology; coherent algebraic sheaves; coherent analytic sheaves; Stein spaces; Fréchet sheaves; Cartan's theorem; projective varieties; Serre's theorems; Dolbeault cohomology; chains of syzygies; Cartan's factorization; amalgamation of syzygies; algebraic groups; Borel-Weil-Bott theorem; equivariant line bundles; flag variety; Casimir operator J. L. Taylor, \textit{Several Complex Variables with Connections to Algebraic Geometry and Lie groups}, Graduate Studies in Mathematics, \textbf{46}, AMS, Providence, RI, 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. quotient spaces of Hilbert modular groups of totally real number fields | 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; vertex algebras Lehn, M.: Lectures on hilbert schemes. CRM Proc Lect Notes \textbf{38}, 1-30 | 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; categories of modules; actions of general linear groups; Auslander-Reiten translations; irreducible components; indecomposable directing modules; normal varieties; degenerations; short exact sequences; module varieties Bobiński, G., Orbit closures of directing modules are regular in codimension one, J. lond. math. soc. (2), 79, 211-224, (2009) | 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. deforming algebras of functions; quantum groups; noncommutative spaces; categories of graded modules Vancliff M., Algebras and representation 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; hereditary Abelian categories; quasitilted algebras of canonical type; categories of coherent sheaves; tilting objects; endomorphism rings; sincere separating families of semiregular standard tubes; Auslander-Reiten components; tame representation type Lenzing, H.; Skowroński, A., Quasi-tilted algebras of canonical type, Colloq. Math., 71, 161-181, (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. Gross-Zagier formula; heights of Heegner points on modular curves; derivatives of \(L\)-series of cusp forms; Hilbert modular form; Automorphic forms on GL(2); Rankin-Selberg \(L\)-function; kernel functions; Geometric pairing of CM-cycles; Shimura curves and CM-points Zhang, SW, Gross-Zagier formula for \(GL_2\), Asian J. Math., 5, 183-290, (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. Galois group; inverse Galois theory; Mathieu groups; finite simple groups; embedding problems; rigidity method; Hilbertian fields; function fields; absolute Galois group; generating polynomials of Galois groups | 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 groups; moduli space of simple holomorphic bundles S. Kosarew and C. Okonek, Global moduli spaces and simple holomorphic bundles, Mathematica Gottingensis, Heft 10, 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. Hilbert modular forms; Eisenstein series; rationality conjecture; special values of Hecke L-functions of CM-fields | 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 classical groups; fixed point ratios; primitive permutation groups; monodromy groups; permutation representations; finite almost simple groups; maximal subgroups of classical groups Timothy C. Burness, Fixed point ratios in actions of finite classical groups. III, J. Algebra 314 (2007), no. 2, 693 -- 748. , https://doi.org/10.1016/j.jalgebra.2007.01.011 Timothy C. Burness, Fixed point ratios in actions of finite classical groups. IV, J. Algebra 314 (2007), no. 2, 749 -- 788. | 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. dimension of a reductive algebraic group; semi-simple 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. Exposés de séminaires; Bourbaki; locally compact groups; cohomology of groups; Riemann-Roch theorem; automorphic functions; compact Lie groups; homotopy groups; fibred algebraic spaces; Albanese varieties | 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 PI-algebras; affine algebraic groups; prime ideals; multiplicity free actions; group actions; Hopf algebras of regular functions; prime spectra; algebras of invariants | 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 double point; McKay correspondence; Dynkin diagram; characteristic p Gonzalez-Sprinberg, G.; Verdier, J. -L.: Structure multiplicative de modules réflexifs sur LES points doubles rationnels. Travaux en cours 22, 79-100 (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. cohomology of finite Chevalley groups; cohomology stability; connected split reductive group scheme; change of fields; algebra retract; elementary abelian \(\ell \)-subgroups; cohomology algebras; integral cohomology; cohomological restriction map | 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. monads; higher Chow complex; operads; unital \(k\)-algebras; little \(n\)-cubes operad; tensor category; braid algebras; mixed Tate motives; symmetric monoidal category; operad of spaces; iterated loop spaces; higher Chow groups; Adams operations; derived category; integral mixed Tate modules; derived categories of modules; DGA; triangulated category; Tannakian category; Hopf algebra; co-Lie algebra; Beilinson-Soulé conjecture; operadic tensor product; cellular approximation theorem Kriz, I.; May, J. P., Operads, algebras, modules and motives, Astérisque, 233, (1995), iv+145 pp | 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 classical groups; fixed point ratios; primitive permutation groups; monodromy groups; permutation representations; finite almost simple groups; maximal subgroups of classical groups DOI: 10.1016/j.jalgebra.2006.05.024 | 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. singularities of Schubert varieties; flag varieties; Dynkin quivers; Cohen-Macaulay varieties Bobiński, Grzegorz; Zwara, Grzegorz, Schubert varieties and representations of Dynkin quivers, Colloq. Math., 94, 2, 285-309, (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. surface singularities of finite Buchsbaum-representation type Shiro Goto, Surface singularities of finite Buchsbaum-representation type, Commutative algebra (Berkeley, CA, 1987) Math. Sci. Res. Inst. Publ., vol. 15, Springer, New York, 1989, pp. 247 -- 263. | 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, affine algebraic group; Borel subgroup; Weyl's character formula; induced modules; global sections of line bundles on the quotient variety; good filtration; rational G-module; group cohomology; derived functors of induction; parabolic subgroups; Kempf's vanishing theorem; exceptional groups; Dynkin diagram; dominant weight; reductive group S. Donkin, \textit{Rational Representations of Algebraic Groups}, Lecture Notes in Mathematics, Vol. 1140, Springer-Verlag, Berlin, 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. cohomology of projective schemes; cohomological Hilbert functions; Castelnuovo--Mumford regularity Brodmann, M.; Lashgari, A. F.: A diagonal bound for cohomological postulation numbers of projective schemes. J. algebra 265, 631-650 (2003) | 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. tame representation type; wild algebras; varieties of algebras; finite axiomatizability; quantifier elimination | 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. algebras of invariants; actions of finite Abelian Hopf algebras; formal groups; regular local rings | 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; affine varieties; general linear groups; degenerations of modules; partial orders; categories of quasi-tubes; minimal degenerations Skowroński, A.; Zwara, G.: On degenerations of modules with nondirecting indecomposable summands. Canad. J. Math. 48, 1091-1120 (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. linear actions of reductive algebraic groups; semisimple Lie algebras Popov, V.: Self-dual algebraic varieties and nilpotent orbits, Tata inst. Fund. res., 509-533 (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. algebraic groups of Mumford-Tate type; Hodge cycles; simple complex abelian variety; Hodge 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. braided Hopf algebras; Nichols-Woronowicz algebras; Schubert calculus; cohomology rings of flag manifolds; coinvariant algebras; finite Coxeter groups; Yetter-Drinfeld categories Y. Bazlov, Nichols--Woronowicz algebra model for Schubert calculus on Coxeter groups, J. Algebra 297 (2006), no. 2, 372--399. | 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. measure; integral; geometry concentration; representations of finite groups; varieties, Nullstellensatz; Bézout inequality; Hilbert basis; Borsuk-Ulam theorem; homotopy; homology | 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. zeta functions of curves over finite fields; factorization of polynomials; cyclotomic polynomials; Aurifeuillian identity; groups of rational points on Jacobians I. Duursma, Class numbers for some hyperelliptic curves, in Arithmetic, Geometry and Coding Theory, Luminy, 1993 (de Gruyter, Berlin, 1996), pp. 45--52 | 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. homogeneous spaces; the Chow group; rational equivalence; simple algebras; Hilbert schemes Daniel Krashen, ``Zero cycles on homogeneous varieties'', Adv. Math.223 (2010) no. 6, p. 2022-2048 | 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 schemes; Hecke algebras; Grassmannians; flag manifolds; preserve sheaves; reductive groups; finite ground fields; local ground fields Gaitsgory, D., \textit{construction of central elements in the affine Hecke algebra via nearby cycles}, Invent. Math., 144, 253-280, (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. Abhyankar conjecture; simple Lie algebras; inverse Galois problem; étale fundamental groups; étale covers | 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 Lie groups; algebraic groups; affine and projective algebraic varieties; algebraic tori; Jordan decomposition; Borel groups; compact linear groups; complete reducibility; root systems; Dynkin diagrams; Cartan decomposition; Iwasawa decomposition; finite dimensional Lie algebra; weight lattices A. Onishchik and E. Vinberg \textit{Lie groups and algebraic groups. }Translated from the Russian and with a preface by D. A. Leites. Springer Series in Soviet Mathematics. Springer-Verlag, Berlin, 1990.Zbl 0722.22004 MR 1064110 | 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 wedge representation; residues of differentials on curves; traces of linear operators; vector spaces of adeles; residue; theorem; cohomology groups; infinite-dimensional Lie algebras; infinite- dimensional groups; Weil pairing on curves; infinite; wedge representations; reciprocity law Arbarello, E., de Concini, C., Kac, V.G.: The infinite wedge representation and the reciprocity law for algebraic curves. In: Proceeding of Symposia in pure mathematics, \textbf{49}, 171-190 (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. homogeneous vector bundles; holomorphic functions; Lie groups; complex analysis; Lie group actions; complex spaces; Lie homomorphism; Lie algebra; automorphism group; compact homogeneous complex manifolds; flag manifolds; normalizer theorem; Tits fibration; induced representations; characters; linear algebraic group; complexification; Fourier expansion; Fréchet vector spaces; geometric invariant theory D. Akhiezer, \textit{Lie Group Actions in Complex Analysis}, Aspects in Math., Vol. 27, Vieweg, 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. Kazhdan-Lusztig polynomials; Schubert varieties; representations of semisimple Lie algebras; Weyl groups; symmetric groups; flag varieties; semisimple groups; torus actions \beginbarticle \bauthor\binitsS. C. \bsnmBilley and \bauthor\binitsT. \bsnmBraden, \batitleLower bounds for Kazhdan-Lusztig polynomials from patterns, \bjtitleTransform. Groups \bvolume8 (\byear2003), no. \bissue4, page 321-\blpage332. \endbarticle \OrigBibText Sara C. Billey and Tom Braden, Lower bounds for Kazhdan-Lusztig polynomials from patterns , Transform. Groups 8 (2003), no. 4, 321-332. \endOrigBibText \bptokstructpyb \endbibitem | 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 simple algebras; index changes under field extensions; function fields; homogeneous varieties; reductive algebraic groups Merkurjev, A.: Degree formula. Available at http://www.mathematik.uni-bielefeld.de/rost/degree-formula.html | 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. root systems; connected reductive algebraic group; projective variety; Borel subgroups; line bundles; orbits; tangent bundle; Weyl group; maximal tori; \(\ell\)-adic cohomology groups; virtual representation; characters; irreducible representations; multiplicities; irreducible components; intersection cohomology; Schubert cells; Weyl groups; Hecke algebras; enveloping algebras; complex reductive Lie algebras; unipotent representations G. Lusztig. Characters of reductive groups over a finite field, Ann. Math. Studies 107, Princeton University Press, 1984. ''BN13N22'' -- 2018/1/30 -- 14:57 -- page 225 -- #27 2018] QUANTIZATIONS OF REGULAR FUNCTIONS ON NILPOTENT ORBITS 225 | 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 abelian cover; cohomology class; extension of the fundamental groups | 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 curves; classification of Hilbert modular surfaces Bassendowski, D.: Klassifikation Hilbertscher Modulflächen zur symmetrischen Hurwitz-Maass-Erweiterung. Dissertation, Bonn, 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. quadratic space; conic bundle surface; resolution of singularities; orders in quaternion 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. quiver representations; finite representation type; infinite representation type; quiver varieties; Hall 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. theta functions; bounded symmetric domains; imaginary quadratic number fields; rings of integers; lattices; modular forms K. Matsumoto: Algebraic relations among some theta functions on the bounded symmetric domain of type \(I_r,r\) , Kyushu J. Math. 60 (2006), 63--77. | 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. Hasse invariants; Eisenstein series; Coleman-Mazur eigencurve; overconvergent modular eigenforms of finite slope DOI: 10.2140/ant.2008.2.209 | 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. annihilation of Selmer groups; adjoint representation; modular forms of weight 2 | 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. singularities of maps; critical points of functions; monodromy; discriminants; stability; normal forms; mixed Hodge structure; characteristic classes Arnol'd, V. I.; Vasil'ev, V. A.; Goryunov, V. V.; Lyashko, O. V.: Singularities local and global theory in dynamical systems. Enc. math. Sc. 6 (1991) | 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 variety; Chow variety; geometric invariant theory; actions of algebraic groups; Chow quotient M. M. Kapranov, B. Sturmfels, and A. V. Zelevinsky, ''Quotients of toric varieties,'' Math. Ann., vol. 290, iss. 4, pp. 643-655, 1991. | 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 Hodge structures; limit of Hodge structures; nilpotent orbit; log geometry; log Riemann-Hilbert correspondence Kazuya Kato, Toshiharu Matsubara, and Chikara Nakayama, Log \?^{\infty }-functions and degenerations of Hodge structures, Algebraic geometry 2000, Azumino (Hotaka), Adv. Stud. Pure Math., vol. 36, Math. Soc. Japan, Tokyo, 2002, pp. 269 -- 320. | 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 groups; maximal orders; Azumaya algebras; regular Noetherian integral schemes; smooth complex affine varieties Antieau, B.; Williams, B.: On the non-existence of Azumaya maximal orders. Invent. math. 197, No. 1, 47-56 (2014) | 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. non-isolated hyperplane singularities; topology of the Milnor fibre; homotopy type of the Milnor fibre | 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 groups of fields of invariants; Galois cohomology; Artin-Mumford group of the field of rational functions Bogomolov F.A., Brauer groups of fields of invariants of algebraic groups, Math. USSR-Sb., 1990, 66(1), 285--299 | 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. homogeneous spaces; rational points; non-abelian cohomology; finite simple groups | 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. textbook (functions of complex variables); Riemann surfaces; harmonic functions; uniformization; functions of several complex variables; abelian functions; modular forms Freitag B., Complex Analysis (2009) | 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. dual graphs; Hilbert schemes; Kontsevich moduli spaces of stable maps; stacks Harris, J; Roth, M; Starr, J, Rational curves on hypersurfaces of low degree, J. Reine Angew. Math., 571, 73-106, (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. Shimura curves; QM type abelian surfaces; Picard modular forms; hypergeometric functions; false elliptic curves; complex multiplication | 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. supergeometry; AdS/CFT correspondence; representations of Lie superalgebras; twistor theory; scattering amplitudes | 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. real algebraic geometry; real algebraic varieties; complexification; Smith's theory; Galois-Maximal varieties; algebraic cycles; real algebraic models; algebraic curves; algebraic surfaces; topology of algebraic varieties; regular maps; rational maps; singularities; algebraic approximation; Comessatti theorem; Rokhlin theorem; Nash conjecture; Hilbert's XVI problem; Cremona group; real fake planes | 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; anisotropic groups; projective spaces; simple connected groups; Zariski topology; maximal torus; root system; group schemes B. Weisfeiler, ''On abstract homomorphisms of anisotropic algebraic groups over real-closed fields,'' J. Algebra,60, No. 2, 485--519 (1979). | 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. Noether-Lefschetz theorem; nontrivial complete intersection curves contained in a general hypersurface; Hilbert schemes; Hilbert functions Szabó, E.: Complete intersection subvarieties of general hypersurfaces, Pacific J. Math. 175, No. 1, 271-294 (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. Kummer surfaces; resolving singularities of the quotient of a complex torus by a finite abelian group; Euler numbers; toroidal desingularization; string J. Halverson, C. Long and B. Sung, \textit{Algorithmic universality in F-theory compactifications}, \textit{Phys. Rev.}\textbf{D 96} (2017) 126006 [arXiv:1706.02299] [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. rings of differential operators; semisimple Lie algebras; gluing of categories DOI: 10.1017/S1474748002000154 | 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. morphism of affine schemes; Hilbert polynomial; locally free module Laksov, D., Pitteloud, Y. andSkjelnes, R. M., Notes on flatness and the Quot functor on rings,Comm. Algebra 28 (2000), 5613--5627. | 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; derived categories; stacks; Hilbert scheme; Brauer group Chen, J-C; Tseng, H-H, A note on derived mckay correspondence, Math. Res. Lett., 15, 435-445, (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. non-associative algebras; problem of Albert; invariant bilinear forms; nil-algebras; solvable algebras; polynomial endomorphisms; Jacobian conjecture | 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. curves over finite fields; zeta-functions of curves; Abelian varieties over finite fields Katz, N.: Spacefilling curves over finite fields. Mrl 6, 613-624 (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. Siegel series; local intersection multiplicity; Gross-Keating invariant; modular correspondence; Siegel-Eisenstein series | 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. surfaces of general type; automorphism groups; cohomology Cai, J.-X., Automorphisms of an irregular surface of general type acting trivially in cohomology, J. Algebra, 367, 95-104, (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. algebraic group schemes; non-reduced group schemes; minimal splitting fields; Galois groups; coordinate rings; groups of rational characters; maximal tori; connected unipotent groups; products of reductions | 0 |
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