$BC_n$-symmetric abelian functions

By Eric M. Rains. 2004

108 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Applied Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ba6ee23944b18f83456961f8b020c7d24c247609

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In Algebra and Number Theory

In Applied Mathematics

In Statistical and Nonlinear Physics

Citations in the corpus

Elliptic Hypergeometry of Supersymmetric Dualities (2009, background): “Limits of the elliptic hypergeometric integrals (or of the elliptic hypergeometric series hidden behind them) matched with the elliptic curve degenerations brought to light new types of q-hypergeometric functions as well [66, 67] (see also [10]).”
Essays on the theory of elliptic hypergeometric functions (2008, methodology): “Sufficiently many applications of elliptic hypergeometric functions in mathematical physics are known at present: in the exactly solvable models of statistical mechanics related to the elliptic solutions of the Yang–Baxter equation [8] and the Sklyanin algebra [ 35 , 79, 80, 116], in nonlinear integ”