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...

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Bibliographic Details
Published in:Symmetry, integrability and geometry, methods and applications Vol. 3; p. 056
Main Author: Schlosser, Michael J.
Format: Journal Article
Language:English
Published: Kiev National Academy of Sciences of Ukraine 01.01.2007
National Academy of Science of Ukraine
Subjects:
6phi_5$ summation
A_{n-1}$ series
basic hypergeometric series
Jackson's _8phi_7$ summation
Macdonald polynomials
matrix inversion
Pieri formula
recursion formula
ISSN:1815-0659, 1815-0659
Online Access:Get full text
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Summary: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?5 summation formula. We derive several new related identities including multivariate extensions of Jackson's very-well-poised 8?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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ISSN:1815-0659
1815-0659
DOI:10.3842/SIGMA.2007.056