{
  "id": "1212.2960",
  "version": "v3",
  "published": "2012-12-12T11:48:13.000Z",
  "updated": "2013-09-08T13:10:27.000Z",
  "title": "Macdonald operators at infinity",
  "authors": [
    "Maxim Nazarov",
    "Evgeny Sklyanin"
  ],
  "comment": "References added. Uses basic facts about symmetric functions also used in arXiv:1212.2781",
  "categories": [
    "math.CO",
    "math.QA",
    "math.RT",
    "nlin.SI"
  ],
  "abstract": "We construct a family of pairwise commuting operators such that the Macdonald symmetric functions of infinitely many variables $x_1,x_2,...$ and of two parameters $q,t$ are their eigenfunctions. These operators are defined as limits at $N\\to\\infty$ of renormalised Macdonald operators acting on symmetric polynomials in the variables $x_1,...,x_N$. They are differential operators in terms of the power sum variables $p_n=x_1^n+x_2^n+...$ and we compute their symbols by using the Macdonald reproducing kernel. We express these symbols in terms of the Hall-Littlewood symmetric functions of the variables $x_1,x_2,...$. Our result also yields elementary step operators for the Macdonald symmetric functions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-09-08T13:10:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "macdonald symmetric functions",
      "yields elementary step operators",
      "hall-littlewood symmetric functions",
      "power sum variables",
      "renormalised macdonald operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.2960N"
    }
  }
}