Decorated tangles and canonical bases

Abstract

We 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 figures