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Equations in Dual Variables for Whittaker Functions

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Abstract

It is known that the Whittaker functions w(qλ) 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 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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  1. Laboratoire de Physique Théorique et Hautes Energies, LPTHE Universités Paris VI-Paris VII (UMR 7589), 4 place Jussieu, F-75252, Paris Cedex 05, France

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Babelon> , O. Equations in Dual Variables for Whittaker Functions. Letters in Mathematical Physics 65, 229–240 (2003). https://doi.org/10.1023/B:MATH.0000010714.56215.2a

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