Theorems · Theorem · group theory

Representation.averageMap_id

∀ {k : Type u_1} {G : Type u_2} {V : Type u_3} [inst : CommRing k] [inst_1 : Group G] [inst_2 : AddCommGroup V]
  [inst_3 : Module k V] (ρ : Representation k G V) [inst_4 : Fintype G] [inst_5 : Invertible ↑(Fintype.card G)],
  ∀ v ∈ ρ.invariants, ρ.averageMap v = v

The averageMap acts as the identity on the subspace of invariants.

Defined in

Mathlib.RepresentationTheory.Invariants

Cited by

1 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupAddCommGroupModuleFintypeInvertible