Theorems · Theorem · group theory

Representation.leftRegular_norm_apply

∀ {k : Type u_1} {G : Type u_2} [inst : CommSemiring k] [inst_1 : Group G] [inst_2 : Fintype G],
  (Representation.leftRegular k G).norm =
    (LinearMap.lsmul k (MonoidAlgebra k G)).flip ((Representation.leftRegular k G).norm (MonoidAlgebra.single 1 1)) ∘ₗ
      (Finsupp.linearCombination k fun x => 1) ∘ₗ ↑(MonoidAlgebra.coeffLinearEquiv k)

Defined in: Mathlib.RepresentationTheory.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring Group Fintype

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Cites36

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
RingHom.idstatement · cited by 18,349
CommSemiringstatement and proof · cited by 10,911
LinearMapstatement · cited by 10,215
Fintypestatement and proof · cited by 7,736
Groupstatement and proof · cited by 6,238
Finsuppstatement · cited by 5,255
Finset.sumproof · cited by 5,195
mul_oneproof · cited by 3,885
Finset.univproof · cited by 3,473
Finset.sum_congrproof · cited by 2,323
LinearMap.compstatement and proof · cited by 1,642

Cited by1

Results whose statement or proof uses this declaration.

Representation.leftRegular_norm_eq_zero_iffproof · cited by 1