{
  "id": "1506.06597",
  "version": "v1",
  "published": "2015-06-22T13:40:13.000Z",
  "updated": "2015-06-22T13:40:13.000Z",
  "title": "A summation formula for Macdonald polynomials",
  "authors": [
    "Jan de Gier",
    "Michael Wheeler"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP",
    "math.RT"
  ],
  "abstract": "We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases $t=1$ and $q=0$, we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively. Other specializations of our formula give new expressions for the Jack and $q$-Whittaker polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-22T13:40:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "summation formula",
      "expression contains multiple sums",
      "explicit sum formula",
      "symmetric macdonald polynomials",
      "whittaker polynomials"
    ],
    "publication": {
      "doi": "10.1007/s11005-016-0820-3",
      "journal": "Letters in Mathematical Physics",
      "year": 2016,
      "month": "Mar",
      "volume": 106,
      "number": 3,
      "pages": 381
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016LMaPh.106..381D"
    }
  }
}