On reconstruction of Veselov–Felder formula in the theory of Calogero–Sutherland operators

A. Matsuo and I. Cherednik proposed the nice construction connecting the solutions of the generalized Knizhnik–Zamolodchikov (KZ) equations with the eigenfunctions of the Calogero–Sutherland operators associated with the same root system. A. Veselov and G. Felder simplified the arguments of the paper of A. Matsuo and I. Cherednik for rational KZ equations and obtained for the root system $A_{n-1}$ the reconstruction formula that permits to get the solution of KZ equation in terms of the eigenfunctions of Calogero operator. In this paper for any reduced irreducible root system the direct proof of the Matsuo–Cherednik assertion on the connection of the solutions of KZ equations with the eigenfunctions of Calogero–Sutherland operators is given, and the reconstruction formula of Felder–Veselov is extended to these root systems.