Factorized solutions of Temperley-Lieb qKZ equations on a segment

Abstract

We study the q-deformed Knizhnik-Zamolodchikov (qKZ) equation in path representations of the Temperley-Lieb algebras. We consider two types of open boundary conditions, and in both cases we derive factorized expressions for the solutions of the qKZ equation in terms of Baxterized Demazurre-Lusztig operators. These expressions are alternative to known integral solutions for tensor product representations. The factorized expressions reveal the algebraic structure within the qKZ equation, and effectively reduce it to a set of truncation conditions on a single scalar function. The factorized expressions allow for an efficient computation of the full solution once this single scalar function is k..