BC_n-symmetric abelian functions

Details BC_n-symmetric abelian functions BC_n-symmetric abelian functions

2004-02-07

arxiv.org/abs/math/0402113v2

Mathematics

Combinatorics

59 pages, LaTeX (with AMS macros). v2: Minor revisions per referee comments

Scientific paper

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 Jackson's summation and Bailey's transformation.

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