Theorems · Theorem · group theory

RootPairing.range_weylGroup_coweightHom

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] (P : RootPairing ι R M N),
  ((RootPairing.Equiv.coweightHom P).domRestrict P.weylGroup).range =
    Subgroup.closure (Set.range (MulOpposite.op ∘ P.coreflection))

Defined in

Mathlib.LinearAlgebra.RootSystem.WeylGroup

Cited by

0 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule