Macdonald Polynomials and Multivariable Basic Hypergeometric Series

Details Macdonald Polynomials and Multivariable Basic Hypergeometric Series Macdonald Polynomials and Multivariable Basic Hypergeometric Series

2006-11-21

arxiv.org/abs/math/0611639v2

SIGMA 3 (2007), 056, 30 pages

Mathematics

Combinatorics

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2007.056

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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