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b797a5b | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | 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)
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
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