Theorems · Theorem · group theory

Representation.char_conj

∀ {G : Type u_1} {k : Type u_2} {V : Type u_3} [inst : Group G] [inst_1 : Field k] [inst_2 : AddCommGroup V]
  [inst_3 : Module k V] (ρ : Representation k G V) (g h : G), ρ.character (h * g * h⁻¹) = ρ.character g

The character of a representation is constant on conjugacy classes.

Defined in

Mathlib.RepresentationTheory.Character

Cited by

0 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupFieldAddCommGroupModule