Representation-theoretic proof of the inner product and symmetry identities for Macdonald's polynomials

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dc.creatorEtingof, Pavel
dc.creatorKirillov Jr, Alexander
dc.date1994-10-21
dc.date.accessioned2026-07-07T09:14:25Z
dc.date.available2026-07-07T09:14:25Z
dc.descriptionThis paper is a continuation of our papers \cite{EK1, EK2}. In \cite{EK2} we showed that for the root system $A_{n-1}$ one can obtain Macdonald's polynomials as weighted traces of intertwining operators between certain finite-dimensional representations of $U_q(sl_n)$. The main goal of the present paper is to use this construction to give a representation-theoretic proof of Macdonald's inner product and symmetry identities for the root system $A_{n-1}$. The proofs are based on the techniques of ribbon graphs developed by Reshetikhin and Turaev. We also use the symmetry identities to derive recursive relations for Macdonald's polynomials.
dc.identifierhttps://arxiv.org/abs/hep-th/9410169
dc.identifierhttp://arxiv.org/abs/hep-th/9410169
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152665
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleRepresentation-theoretic proof of the inner product and symmetry identities for Macdonald's polynomials
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