Macdonald Polynomials and Multivariable Basic Hypergeometric Series

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dc.creatorSchlosser, Michael J.
dc.date2006-11-21
dc.date2007-03-30
dc.date.accessioned2026-07-07T09:34:33Z
dc.date.available2026-07-07T09:34:33Z
dc.descriptionWe 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.
dc.descriptionThis is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/math/0611639
dc.identifierhttp://arxiv.org/abs/math/0611639
dc.identifierSIGMA 3 (2007), 056, 30 pages
dc.identifierdoi:10.3842/SIGMA.2007.056
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159532
dc.subjectCombinatorics
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.subjectQuantum Algebra
dc.subject33D52 (Primary) 15A09, 33D67 (Secondary)
dc.titleMacdonald Polynomials and Multivariable Basic Hypergeometric Series
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