Theorems · Definition · group theory

RootPairing.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) → Representation R (↥P.weylGroup) M

The natural representation of the Weyl group on the root space.

Defined in

Mathlib.LinearAlgebra.RootSystem.WeylGroup

Cited by

2 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule