Integral Solutions of Trigonometric Knizhnik-Zamolodchikov Equations and Kac-Moody Algebras

Abstract

We use Kac-Moody algebras to get some integral solutions for trigonometric r-matrix Knizhnik-Zamolodchikov equations of type X_l⁽¹⁾, generalizing those in the case of Yang's r-matrix, where our construction gives a new interpretation and a short proof of Schechtman, Varchenko theorem.