Equations in dual variables for Whittaker functions

Abstract

It is known that the Whittaker functions $w(q,\lambda )$ associated to the group SL(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 ${\lambda }_i$, 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 ${\lambda }_i$.

13 pages