Theorems · Theorem · nonassociative algebras

RootPairing.isSimpleModule_weylGroupRootRep

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] (P : RootPairing ι R M N) [P.IsIrreducible],
  IsSimpleModule (MonoidAlgebra R ↥P.weylGroup) P.weylGroupRootRep.asModule

Defined in: Mathlib.LinearAlgebra.RootSystem.Irreducible
Cited by: 0 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module RootPairing.IsIrreducible

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Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Subgroupstatement · cited by 3,593
Nontrivialproof · cited by 2,416
RootPairingstatement and proof · cited by 710
MonoidAlgebrastatement · cited by 590
IsSimpleModulestatement · cited by 114
RootPairing.IsIrreduciblestatement and proof · cited by 35
RootPairing.Autstatement · cited by 30
Representation.asModulestatement · cited by 22
RootPairing.weylGroupstatement · cited by 14

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