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arXiv · 1412.0714

A representation-theoretic proof of the branching rule for Macdonald polynomials

Yi Sun
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Abstract

We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of U_q(gl_n). In the Gelfand-Tsetlin basis, we show that diagonal matrix elements of such intertwiners are given by application of Macdonald's operators to a simple kernel. An essential ingredient in the proof is a map between spherical parts of double affine Hecke algebras of different ranks based upon the Dunkl-Kasatani conjecture.

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BibTeXRIS

Yi Sun. 2014-12-01. A representation-theoretic proof of the branching rule for Macdonald polynomials. https://doi.org/10.4310/mrl.2016.v23.n3.a15

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