Theorems · Theorem · group theory

RootPairing.InvariantForm.apply_weylGroup_smul

∀ {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) {B : P.InvariantForm}
  (g : ↥P.weylGroup) (x y : M), (B.form (g • x)) (g • y) = (B.form x) y

Defined in

Mathlib.LinearAlgebra.RootSystem.WeylGroup

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommRingAddCommGroupModuleAddCommGroupModule