Matrix elements of vertex operators of deformed W-algebra and Harish Chandra Solutions to Macdonald's difference equations

Abstract

In this paper we prove that certain matrix elements of vertex operators of deformed W-algebra satisfy Macdonald difference equations and form n! -dimensional space of solutions. These solutions are the analogues of Harish Chandra solutions with prescribed asymptotic behavior. We obtain formulas for analytic continuation as a consequence of braiding properties of vertex operators of deformed W-algebra.