Theorems · Theorem · group theory

FDRep.char_orthonormal

∀ {k : Type u} [inst : Field k] {G : Type v} [inst_1 : Group G] [IsAlgClosed k] [inst_3 : Fintype G]
  [Invertible ↑(Nat.card G)] (V W : FDRep k G) [CategoryTheory.Simple V] [CategoryTheory.Simple W],
  (↑(Nat.card G))⁻¹ * ∑ g, V.character g * W.character g⁻¹ = if Nonempty (V ≅ W) then 1 else 0

Orthogonality of characters for irreducible representations of finite group over an algebraically closed field whose characteristic doesn't divide the order of the group.

Defined in

Mathlib.RepresentationTheory.Character

Cited by

1 results in Mathlib

Foundations

Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldGroupIsAlgClosedFintypeInvertibleCategoryTheory.SimpleCategoryTheory.Simple