## Sun, Yi - A representation-theoretic proof of the branching rule for Macdonald polynomials

dmtcs:2493 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
A representation-theoretic proof of the branching rule for Macdonald polynomials

Authors: Sun, Yi

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.

Source : oai:HAL:hal-01337768v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: Macdonald polynomials,quantum groups,Gelfand-Tsetlin basis,double affine Hecke algebras,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]