Commuting difference operators with polynomial eigenfunctions
funct-an
2008-02-03 v1 High Energy Physics - Theory
Operator Algebras
Exactly Solvable and Integrable Systems
solv-int
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.
Cite
@article{arxiv.funct-an/9306002,
title = {Commuting difference operators with polynomial eigenfunctions},
author = {J. F. van Diejen},
journal= {arXiv preprint arXiv:funct-an/9306002},
year = {2008}
}
Comments
24 pp. (printing format: landscape), Latex (+ amssymbols.sty)