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BC_n-symmetric abelian functions

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.

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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.

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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
Record Number:CaltechAUTHORS:20171003-154931716
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82015
Deposited By: Tony Diaz
Deposited On:04 Oct 2017 18:04
Last Modified:01 Jun 2023 23:58

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