Michael J. Schlosser

Macdonald polynomials and multivariable basic hypergeometric series

(30 pages)

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 ₆Φ₅ summation formula. We derive several new related identities including multivariate extensions of Jackson's very-well-poised ₈Φ₇ 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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