Rains, Eric M. (2006) BC_n-symmetric abelian functions. Duke Mathematical Journal, 135 (1). pp. 99-180. ISSN 0012-7094. doi:10.48550/arXiv.0402113. https://resolver.caltech.edu/CaltechAUTHORS:20171003-154931716
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Abstract
We construct a family of BC_n-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.
| Item Type: | Article | |||||||||
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| Additional Information: | © 2006 Duke University Press. Received 21 April 2005. Revision received 7 February 2006. Author’s work supported in part by National Science Foundation grant DMS-0403187. We thank R. Gustafson, A. Okounkov, H. Rosengren, S. Sahi, and V. Spiridonov for enlightening conversations related to this work. | |||||||||
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| Issue or Number: | 1 | |||||||||
| Classification Code: | 2000 Mathematics Subject Classification: Primary 33D52; Secondary 14H52, 14K25 | |||||||||
| DOI: | 10.48550/arXiv.0402113 | |||||||||
| Record Number: | CaltechAUTHORS:20171003-154931716 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20171003-154931716 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 82015 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 04 Oct 2017 18:04 | |||||||||
| Last Modified: | 01 Jun 2023 23:58 |
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