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Published 2006 | Submitted
Journal Article Open

BC_n-symmetric abelian functions

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.

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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Created:
August 19, 2023
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