Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published 2006 | Submitted
Book Section - Chapter Open

A difference-integral representation of Koornwinder polynomials

Abstract

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.

Additional Information

© 2006 American Mathematical Society. This paper is based on a talk the author gave at the Workshop on Jack, Hall-Littlewood and Macdonald Polynomials held at the International Centre for Mathematical Sciences, September 23 through 26, 2003. The author would like to thank the organizers for inviting him to that stimulating meeting, as well as the other participants for making the meeting stimulating.

Attached Files

Submitted - 0409437.pdf

Files

0409437.pdf
Files (199.2 kB)
Name Size Download all
md5:f3158014ce6e3c7ce29541fe8d67ae20
199.2 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
March 5, 2024