Hypergeometric solutions of trigonometric KZ equations satisfy dynamical difference equations

Abstract

The trigonometric KZ equations associated to a Lie algebra g depend on a parameter λ ∈ h where h ⊂ g is a Cartan subalgebra. A system of dynamical difference equations with respect to λ compatible with the KZ equations is introduced by V. Tarasov and the second author (2000, Internat. Math. Res. Notices 15, 801-829). We prove that the standard hypergeometric solutions of the trigonometric KZ equations associated to slN also satisfy the dynamical difference equations. © 2002 Elsevier Science (USA).