A representation-theoretic proof of the branching rule for Macdonald polynomials
Representation Theory
2016-07-13 v1 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.1412.0714,
title = {A representation-theoretic proof of the branching rule for Macdonald polynomials},
author = {Yi Sun},
journal= {arXiv preprint arXiv:1412.0714},
year = {2016}
}
Comments
22 pages