{
  "id": "1704.02429",
  "version": "v1",
  "published": "2017-04-08T02:56:00.000Z",
  "updated": "2017-04-08T02:56:00.000Z",
  "title": "Asymptotic Formulas for Macdonald Polynomials and the boundary of the $(q, t)$-Gelfand-Tsetlin graph",
  "authors": [
    "Cesar Cuenca"
  ],
  "comment": "50 pages. Comments are welcome",
  "categories": [
    "math.RT",
    "math-ph",
    "math.CA",
    "math.CO",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We introduce Macdonald characters and use algebraic properties of Macdonald polynomials to study them. As a result, we produce several formulas for Macdonald characters, which are generalizations of those obtained by Gorin-Panova in arXiv:1301.0634 [math.PR], and are expected to provide tools for the study of statistical mechanical models, representation theory and random matrices. As first application of our formulas, we characterize the boundary of the $(q, t)-$deformation of the Gelfand-Tsetlin graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-08T02:56:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D52",
      "33D90",
      "60B15",
      "60C05"
    ],
    "keywords": [
      "macdonald polynomials",
      "gelfand-tsetlin graph",
      "asymptotic formulas",
      "macdonald characters",
      "algebraic properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}