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