Theorems · Definition · group theory

Representation.invariantsEquivIntertwiningMap

{k : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      {W : Type u_4} →
        [inst : CommRing k] →
          [inst_1 : Group G] →
            [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.linHom σ).invariants ≃ₗ[k] ρ.IntertwiningMap σ

The invariants of the representation linHom ρ σ correspond to intertwining maps from ρ to σ.

Defined in

Mathlib.RepresentationTheory.Invariants

Cited by

1 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Quot.sound

Assumes

CommRingGroupAddCommGroupModuleAddCommGroupModule