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Bisymmetric functions, Macdonald polynomials and sl_3 basic hypergeometric series

S. Ole Warnaar
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Abstract

A new type of sl_3 basic hypergeometric series based on Macdonald polynomials is introduced. Besides a pair of Macdonald polynomials attached to two different sets of variables, a key-ingredient in the sl_3 basic hypergeometric series is a bisymmetric function related to Macdonald's commuting family of q-difference operators, to the sl_3 Selberg integrals of Tarasov and Varchenko, and to alternating sign matrices. Our main result for sl_3 series is a multivariable generalization of the celebrated q-binomial theorem. In the limit this q-binomial sum yields a new sl_3 Selberg integral for Jack polynomials.

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S. Ole Warnaar. 2007-07-24. Bisymmetric functions, Macdonald polynomials and sl_3 basic hypergeometric series. https://arxiv.org/abs/math/0511333

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