2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62002We study the combinatorics of fully commutative elements in Coxeter groups of type $H_n$ for any $n > 2$. Using the results, we construct certain canonical bases (i.e., IC bases) for non-simply-laced generalized Temperley--Lieb algebras and show how to relate them to morphisms in the category of decorated tangles.45 pages AMSTeX; 13 postscript figuresQuantum Algebra20F55, 20C08, 57M15text