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

1994/10/21 by Pavel Etingof, Etingof, Pavel, Alexander Kirillov Jr +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.QA

paper · pdf · doi:10.48550/arxiv.hep-th/9410169

arxiv created 1994/10/21 · arxiv updated 2009/11/30

Abstract

This paper is a continuation of our papers \citeEK1, EK2. In \citeEK2 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.

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