Bisymmetric functions, Macdonald polynomials and sl_3 basic hypergeometric series

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dc.creatorWarnaar, S. Ole
dc.date2005-11-14
dc.date2007-07-24
dc.date.accessioned2026-07-07T09:39:55Z
dc.date.available2026-07-07T09:39:55Z
dc.descriptionA new type of sl_3 basic hypergeometric series based on Macdonald polynomials is introduced. Besides a pair of Macdonald polynomials attached to two different sets of variables, a key-ingredient in the sl_3 basic hypergeometric series is a bisymmetric function related to Macdonald's commuting family of q-difference operators, to the sl_3 Selberg integrals of Tarasov and Varchenko, and to alternating sign matrices. Our main result for sl_3 series is a multivariable generalization of the celebrated q-binomial theorem. In the limit this q-binomial sum yields a new sl_3 Selberg integral for Jack polynomials.
dc.description33 pages; major revision of earlier, much longer paper; to appear in Compositio Mathematica
dc.identifierhttps://arxiv.org/abs/math/0511333
dc.identifierhttp://arxiv.org/abs/math/0511333
dc.identifierCompositio Math. 144 (2008), 271-303
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161356
dc.subjectCombinatorics
dc.subjectQuantum Algebra
dc.subject05E05, 33D67
dc.titleBisymmetric functions, Macdonald polynomials and sl_3 basic hypergeometric series
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