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Bisymmetric functions, Macdonald polynomials and basic hypergeometric series

  • S. Ole Warnaar (a1)

Abstract

A new type of 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 basic hypergeometric series is a bisymmetric function related to Macdonald’s commuting family of q-difference operators, to the Selberg integrals of Tarasov and Varchenko, and to alternating sign matrices. Our main result for series is a multivariable generalization of the celebrated q-binomial theorem. In the limit this q-binomial sum yields a new Selberg integral for Jack polynomials.

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Work supported by the Australian Research Council.

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Bisymmetric functions, Macdonald polynomials and basic hypergeometric series

  • S. Ole Warnaar (a1)

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