Equations in Dual Variables for Whittaker Functions |
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Authors: | Babelon> O |
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Institution: | (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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Abstract: | 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
. |
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Keywords: | quantum algebra exactly solvable and integrable systems |
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