Theorems · Theorem · group theory

Representation.IsIrreducible.surjective_or_eq_zero

∀ {G : Type u_1} {k : Type u_2} {V : Type u_3} {W : Type u_4} [inst : Monoid G] [inst_1 : Field k]
  [inst_2 : AddCommGroup V] [inst_3 : Module k V] [inst_4 : AddCommGroup W] [inst_5 : Module k W]
  {ρ : Representation k G V} {σ : Representation k G W} [ρ.IsIrreducible] (g : σ.IntertwiningMap ρ),
  Function.Surjective ⇑g ∨ g = 0

Defined in

Mathlib.RepresentationTheory.Irreducible

Cited by

0 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MonoidFieldAddCommGroupModuleAddCommGroupModuleRepresentation.IsIrreducible