Equations in dual variables for Whittaker functions

2003/07/18 by O. Babelon, Babelon, O.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0307037

13 pages

arxiv created 2003/07/18 · arxiv updated 2009/12/01

Abstract

It is known that the Whittaker functions w(q,λ) 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 λ_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 λ_i.

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