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.
Orthogonality of Macdonald polynomials with unitary parameters
Asymptotic Formulas for Macdonald Polynomials and the boundary of the $(q, t)$-Gelfand-Tsetlin graph
Affine Hecke algebras and symmetric quasi-polynomial duality
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