Theorems · Theorem · group theory
Representation.averageMap_invariant
∀ {k : Type u_1} {G : Type u_2} {V : Type u_3} [inst : CommRing k] [inst_1 : Group G] [inst_2 : AddCommGroup V]
[inst_3 : Module k V] (ρ : Representation k G V) [inst_4 : Fintype G] [inst_5 : Invertible ↑(Fintype.card G)] (v : V),
ρ.averageMap v ∈ ρ.invariantsThe averageMap sends elements of V to the subspace of invariants.
- Defined in
- Mathlib.RepresentationTheory.Invariants
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Submodulestatement · cited by 7,192
- Groupstatement and proof · cited by 6,238
- Fintype.cardstatement and proof · cited by 1,386
- map_mulproof · cited by 1,137
- Module.Endproof · cited by 774
Cited by1
Results whose statement or proof uses this declaration.
- Representation.isProj_averageMapproof · cited by 2