Theorems · Theorem · group theory

Representation.finsuppTensorRight_apply_tmul

∀ {G : Type v} [inst : Monoid G] {V : Type v'} [inst_1 : AddCommMonoid V] {W : Type w'} [inst_2 : AddCommMonoid W]
  {k : Type u} [inst_3 : CommSemiring k] [inst_4 : Module k V] [inst_5 : Module k W] (σ : Representation k G V)
  (ρ : Representation k G W) {α : Type w'} [inst_6 : DecidableEq α] (v : V) (f : α →₀ W),
  (σ.finsuppTensorRight ρ α) (v ⊗ₜ[k] f) = f.sum fun i w => fun₀ | i => v ⊗ₜ[k] w

Defined in

Mathlib.RepresentationTheory.Equiv

Cited by

1 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MonoidAddCommMonoidAddCommMonoidCommSemiringModuleModuleDecidableEq