Michael J. Schlosser
Macdonald polynomials and multivariable basic hypergeometric series
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
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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