2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78340We establish the existence of an IC basis for the generalized Temperley--Lieb algebra associated to a Coxeter system of arbitrary type. We determine this basis explicitly in the case where the Coxeter system is simply laced and the algebra is finite dimensional.11 pages, AMSTeXQuantum Algebratext