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Commuting difference operators with polynomial eigenfunctions

J. F. van Diejen
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Abstract

We present explicit generators of an algebra of commuting difference operators with trigonometric coefficients. The operators are simultaneously diagonalized by recently discovered q-polynomials (viz. Koornwinder's multivariable generalization of the Askey-Wilson polynomials). From the viewpoint of physics the algebra can be interpreted as consisting of the quantum integrals of a novel difference-type integrable sytem. This system generalizes the Calogero-Moser systems associated with non-exceptional root systems.

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J. F. van Diejen. 1993-06-07. Commuting difference operators with polynomial eigenfunctions. https://arxiv.org/abs/funct-an/9306002

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