DIS

Abstract

I will report on correspondences between bispectral problems for (1) Ruijsenaars' q-difference equations, (2) Cherednik's q-difference reflection equations, and (3) quantum Knizhnik-Zamolodchikov equations. In addition I will discuss the solutions to these bispectral problems, and their interrelations. An important role in this analysis will be played by Cherednik's q-analog of the spherical function, which solves the bispectral problem of Ruijsenaars' q-difference equations. This talk is partially based on joint work with Michel van Meer.