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A difference-integral representation of Koornwinder polynomials

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Part of book or chapter of book 01 Jan 2004Embargo end date: 01 Jan 2004 United States Publisher:arXiv
Authors: Rains, Eric M.;

doi: 10.48550/arxiv.math/0409437

arXiv: math/0409437

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.

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

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United States
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Keywords

33D52 (05E35), math.CA, 510, Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), math.CO, math.QA

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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