Theorems · Definition · group theory

Rep.quotientToInvariants

{k : Type u} →
  {G : Type v} →
    [inst : CommRing k] →
      [inst_1 : Group G] → Rep.{w, u, v} k G → (S : Subgroup G) → [inst_2 : S.Normal] → Rep.{w, u, v} k (G ⧸ S)

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

3 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupSubgroup.Normal