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Macdonald Polynomials and Multivariable Basic Hypergeometric Series

Michael J. Schlosser
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Abstract

We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials, both represent multivariable extensions of the terminating very-well-poised 6-phi-5 summation formula. We derive several new related identities including multivariate extensions of Jackson's very-well-poised 8-phi-7 summation. Motivated by our basic hypergeometric analysis, we propose an extension of Macdonald polynomials to Macdonald symmetric functions indexed by partitions with complex parts. These appear to possess nice properties.

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BibTeXRIS

Michael J. Schlosser. 2007-03-30. Macdonald Polynomials and Multivariable Basic Hypergeometric Series. https://doi.org/10.3842/sigma.2007.056

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