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arXiv · 1903.01827

Bispectral dual difference equations for the quantum Toda chain with boundary perturbations

J. F. van Diejen·E. Emsiz
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Abstract

We show that hyperoctahedral Whittaker functions---diagonalizing an open quantum Toda chain with one-sided boundary potentials of Morse type---satisfy a dual system of difference equations in the spectral variable. This extends a well-known bispectral duality between the nonperturbed open quantum Toda chain and a strong-coupling limit of the rational Macdonald-Ruijsenaars difference operators. It is manifest from the difference equations in question that the hyperoctahedral Whittaker function is entire as a function of the spectral variable.

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J. F. van Diejen, E. Emsiz. 2019-03-05. Bispectral dual difference equations for the quantum Toda chain with boundary perturbations. https://doi.org/10.1093/imrn%2Frnx219

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