Macdonald Polynomials and Multivariable Basic Hypergeometric Series

Michael J. Schlosser

Symmetry, integrability and geometry: methods and applications, Tome 3 (2007)

Résumé

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.

Détail

Keywords: Macdonald polynomials; Pieri formula; recursion formula; matrix inversion; basic hypergeometric series; ${}_6\phi_5$ summation; JacksonвЂTMs ${}_8\phi_7$ summation; $A_{n-1}$ series.

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