| import Mathlib |
| import OAI.NumberTheory.PrimePackets.AdelicContinuity |
|
|
| namespace OAI |
|
|
| noncomputable section |
| open scoped TensorProduct Topology MatrixGroups |
| open Matrix Module Set |
| namespace PrimeDegreePackets.Adelic |
| |
| |
| instance realPGLTopology (n : ℕ) : TopologicalSpace PGL(Fin n, ℝ) := |
| inferInstanceAs (TopologicalSpace (GL (Fin n) ℝ ⧸ Subgroup.center (GL (Fin n) ℝ))) |
| instance realPGLTopologicalGroup (n : ℕ) : IsTopologicalGroup PGL(Fin n, ℝ) := |
| inferInstanceAs (IsTopologicalGroup (GL (Fin n) ℝ ⧸ Subgroup.center (GL (Fin n) ℝ))) |
|
|
| |
| def realTorus {n : ℕ} {K : Type*} [Field K] [NumberField K] |
| (b : Basis (Fin n) ℚ K) : Subgroup PGL(Fin n, ℝ) := |
| (ProjGenLinGroup.mk.comp (rowRegularUnits (b.baseChange ℝ))).range |
|
|
| |
| def realTorusIdentity {n : ℕ} {K : Type*} [Field K] [NumberField K] |
| (b : Basis (Fin n) ℚ K) : Set PGL(Fin n, ℝ) := |
| (fun t : realTorus b => (t : PGL(Fin n, ℝ))) '' connectedComponent (1 : realTorus b) |
|
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| |
| def AllowedRealDiagonalizer {n : ℕ} {K : Type*} [Field K] [NumberField K] |
| (b : Basis (Fin n) ℚ K) (h : PGL(Fin n, ℝ)) : Prop := |
| (fun t => h⁻¹ * t * h) '' realTorusIdentity b = |
| SpecialLinearGroup.toPGL '' positiveDiagonal n |
|
|
| end PrimeDegreePackets.Adelic |
|
|
| end |
|
|
| end OAI |
| |
