Equations in dual variables for Whittaker functions

Details Equations in dual variables for Whittaker functions Equations in dual variables for Whittaker functions

2003-07-18

arxiv.org/abs/math-ph/0307037v1

Physics

Mathematical Physics

13 pages

Scientific paper

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 $\lambda_i$.

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