# $BC_n$-symmetric abelian functions

@article{Rains2004BC\_nsymmetricAF,
title={\$BC\_n\$-symmetric abelian functions},
author={Eric M. Rains},
journal={Duke Mathematical Journal},
year={2004},
volume={135},
pages={99-180}
}
• E. Rains
• Published 2004
• Mathematics
• Duke Mathematical Journal
We construct a family of BC_n-symmetric biorthogonal abelian functions generalizing Koornwinder's orthogonal polynomials, 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. We show that these interpolation functions satisfy a collection of generalized hypergeometric identities, including new multivariate elliptic analogues of… Expand
56 Citations
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