Equations in Dual Variables for Whittaker Functions

It is known that the Whittaker functions w(q) associated with the group GL(N) are eigenfunctions of the Hamiltonians of the open Toda chain, hence satisfy a set of differential equations in the Toda variables q_i. Using the expression of the q_i for the closed Toda chain in terms of Sklyanin variables _i, and the known relations between the open and the closed Toda chains, we show that Whittaker functions also satisfy a set of new difference equations in _i.