Theorems · Definition · group theory

Representation.quotientToInvariants

{k : Type u_1} →
  {G : Type u_2} →
    [inst : CommRing k] →
      [inst_1 : Group G] →
        {V : Type u_5} →
          [inst_2 : AddCommGroup V] →
            [inst_3 : Module k V] →
              (ρ : Representation k G V) →
                (S : Subgroup G) →
                  [inst_4 : S.Normal] →
                    Representation k (G ⧸ S) ↥(Representation.invariants (MonoidHom.comp ρ S.subtype))

Given a normal subgroup S ≤ G, a G-representation ρ induces a G ⧸ S-representation on the invariants of ρ|_S.

Defined in

Mathlib.RepresentationTheory.Invariants

Cited by

1 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupAddCommGroupModuleSubgroup.Normal