{
  "id": "1412.0714",
  "version": "v1",
  "published": "2014-12-01T22:33:26.000Z",
  "updated": "2014-12-01T22:33:26.000Z",
  "title": "A representation-theoretic proof of the branching rule for Macdonald polynomials",
  "authors": [
    "Yi Sun"
  ],
  "comment": "22 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-01T22:33:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D52",
      "33D80",
      "20C08"
    ],
    "keywords": [
      "macdonald polynomials",
      "representation-theoretic proof",
      "branching rule",
      "double affine hecke algebras",
      "diagonal matrix elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.0714S"
    }
  }
}