Solutions of Trigonometric KZ Equations satisfy Dynamical Difference Equations

Abstract

The trigonometric KZ equations associated to a Lie algebra \g depend on a parameter λin \h where \h is a Cartan subalgebra of \g. A system of dynamical difference equations with respect to λcompatible with the KZ equations is introduced in Tarasov and Varchenko. We prove that the standard hypergeometric solutions of the trigonometric KZ equations associated to sl_N also satisfy the dynamical difference equations.

AMS-LaTeX, 38 pages, 9 figures