Commuting difference operators with polynomial eigenfunctions

Details Commuting difference operators with polynomial eigenfunctions Commuting difference operators with polynomial eigenfunctions

1993-06-07

arxiv.org/abs/funct-an/9306002v1

Comp. Math. 95 (1995) 183-233

Physics

High Energy Physics

High Energy Physics - Theory

24 pp. (printing format: landscape), Latex (+ amssymbols.sty)

Scientific paper

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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