Published 2006
| Submitted
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A difference-integral representation of Koornwinder polynomials
- Creators
-
Rains, Eric M.
- Others:
- Kuznetsov, Vadim B.
- Sahi, Siddhartha
Chicago
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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
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Additional details
- Eprint ID
- 82253
- DOI
- 10.1090/conm/417/07929
- Resolver ID
- CaltechAUTHORS:20171010-105435263
- Created
-
2017-10-10Created from EPrint's datestamp field
- Updated
-
2021-11-15Created from EPrint's last_modified field
- Series Name
- Contemporary Mathematics
- Series Volume or Issue Number
- 417