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1 October 2006 BCn-symmetric abelian functions
Eric M. Rains
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Duke Math. J. 135(1): 99-180 (1 October 2006). DOI: 10.1215/S0012-7094-06-13513-5

Abstract

We construct a family of BCn-symmetric biorthogonal abelian functions generalizing Koornwinder's orthogonal polynomials (see [10]) and prove a number of their properties, most notably analogues of Macdonald's conjectures. The construction is based on a direct construction for a special case generalizing Okounkov's interpolation polynomials (see [13]). We show that these interpolation functions satisfy a collection of generalized hypergeometric identities, including new multivariate elliptic analogues of Jackson's summation and Bailey's transformation

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Eric M. Rains. "BCn-symmetric abelian functions." Duke Math. J. 135 (1) 99 - 180, 1 October 2006. https://doi.org/10.1215/S0012-7094-06-13513-5

Information

Published: 1 October 2006
First available in Project Euclid: 26 September 2006

zbMATH: 1101.33012
MathSciNet: MR2259924
Digital Object Identifier: 10.1215/S0012-7094-06-13513-5

Subjects:
Primary: 33D52
Secondary: 14H52 , 14K25

Rights: Copyright © 2006 Duke University Press

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Vol.135 • No. 1 • 1 October 2006
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