Theorems · Theorem · group theory

Representation.card_inv_mul_sum_char_eq_finrank

∀ {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] [FiniteDimensional k V] (ρ : Representation k G V) [inst_5 : Fintype G]
  [Invertible ↑(Nat.card G)], (↑(Nat.card G))⁻¹ * ∑ g, ρ.character g = ↑(Module.finrank k ↥ρ.invariants)

Defined in

Mathlib.RepresentationTheory.Character

Cited by

1 results in Mathlib

Foundations

Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupFieldAddCommGroupModuleFiniteDimensionalFintypeInvertible