Theorems · Definition · Lie groups

ContIntertwiningMap.mapInvariantsOfRes

{R : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      {W : Type u_4} →
        [inst : Monoid G] →
          [inst_1 : Ring R] →
            [inst_2 : AddCommGroup V] →
              [inst_3 : TopologicalSpace V] →
                [inst_4 : IsTopologicalAddGroup V] →
                  [inst_5 : Module R V] →
                    [inst_6 : AddCommGroup W] →
                      [inst_7 : TopologicalSpace W] →
                        [inst_8 : IsTopologicalAddGroup W] →
                          [inst_9 : Module R W] →
                            {H : Type u_6} →
                              [inst_10 : Monoid H] →
                                {π : ContRepresentation R G V} →
                                  {π' : ContRepresentation R H W} →
                                    (φ : H →* G) →
                                      ContIntertwiningMap (π.restrict φ) π' → ↥π.invariants →L[R] ↥π'.invariants

Given a monoid homomorphism φ : H →* G, a G-representation π and an H-representation π', a continuous intertwining map f : π.restrict φ →ⁱL π' induces a continuous linear map π.invariants →L[R] π'.invariants between the invariant submodules.

Defined in

Mathlib.RepresentationTheory.Continuous.Basic

Cited by

3 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MonoidRingAddCommGroupTopologicalSpaceIsTopologicalAddGroupModuleAddCommGroupTopologicalSpaceIsTopologicalAddGroupModuleMonoid