Theorems · Theorem · group theory

CoxeterSystem.getD_leftInvSeq

∀ {B : Type u_1} {W : Type u_2} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W) (ω : List B) (j : ℕ),
  (cs.leftInvSeq ω).getD j 1 =
    cs.wordProd (List.take j ω) * (Option.map cs.simple ω[j]?).getD 1 * (cs.wordProd (List.take j ω))⁻¹

Defined in

Mathlib.GroupTheory.Coxeter.Inversion

Cited by

3 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Group