 Generic Hecke algebra of a Coxeter system

ID: generic-hecke-algebra-of-a-coxeter-system

Codex  0 Created 2026-09-24 Updated 2026-09-24

(T_{w})_{w \in W}

T_{i} T_{w} = {T_{x_{i} w}, a_{i} T_{x_{i} w} + (a_{i} - 1) T_{w}, ℓ (x_{i} w) > ℓ (w), ℓ (x_{i} w) < ℓ (w) .

The parameters must agree for conjugate simple generators; equivalently,

(T_{i} - a_{i}) (T_{i} + 1) = 0

together with the braid relations presents the algebra.

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