93-170 van Diejen, J. F.
Commuting difference operators with polynomial eigenfunctions. (149K, LaTex (printing format: landscape)) Jun 8, 93
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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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