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