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Bisymmetric functions, Macdonald polynomials and
basic hypergeometric series
- Part of
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- Journal:
- Compositio Mathematica / Volume 144 / Issue 2 / March 2008
- Published online by Cambridge University Press:
- 01 March 2008, pp. 271-303
- Print publication:
- March 2008
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- Article
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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.
basic hypergeometric series
