Theorems · Definition · group theory

Representation.subrepresentation

{k : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      [inst : Semiring k] →
        [inst_1 : Monoid G] →
          [inst_2 : AddCommMonoid V] →
            [inst_3 : Module k V] →
              (ρ : Representation k G V) →
                (W : Submodule k V) → (∀ (g : G), W ≤ Submodule.comap (ρ g) W) → Representation k G ↥W

Given a k-linear G-representation (V, ρ), this is the representation defined by restricting ρ to a G-invariant k-submodule of V.

Defined in

Mathlib.RepresentationTheory.Basic

Cited by

2 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Quot.sound

Assumes

SemiringMonoidAddCommMonoidModule