Theorems · Theorem · group theory

Representation.IsIrreducible.finrank_intertwiningMap_self

∀ {G : Type u_1} {k : Type u_2} {V : Type u_3} [inst : Monoid G] [inst_1 : Field k] [inst_2 : AddCommGroup V]
  [inst_3 : Module k V] (ρ : Representation k G V) [ρ.IsIrreducible] [FiniteDimensional k V] [IsAlgClosed k],
  Module.finrank k (ρ.IntertwiningMap ρ) = 1

Defined in

Mathlib.RepresentationTheory.Irreducible

Cited by

1 results in Mathlib

Foundations

Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MonoidFieldAddCommGroupModuleRepresentation.IsIrreducibleFiniteDimensionalIsAlgClosed