A difference-integral representation of Koornwinder polynomials

Details A difference-integral representation of Koornwinder polynomials A difference-integral representation of Koornwinder polynomials

2004-09-22

arxiv.org/abs/math/0409437v1

Mathematics

Classical Analysis and ODEs

15 pages AMSLaTeX. To appear in proceedings of the Workshop on Jack, Hall-Littlewood and Macdonald polynomials (September 2003

Scientific paper

We construct new families of (q-) difference and (contour) integral operators having nice actions on Koornwinder's multivariate orthogonal polynomials. We further show that the Koornwinder polynomials can be constructed by suitable sequences of these operators applied to the constant polynomial 1, giving the difference-integral representation of the title. Macdonald's conjectures (as proved by van Diejen and Sahi) for the principal specialization and norm follow immediately, as does a Cauchy-type identity of Mimachi.

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