{
  "id": "0803.1146",
  "version": "v1",
  "published": "2008-03-05T18:01:43.000Z",
  "updated": "2008-03-05T18:01:43.000Z",
  "title": "A combinatorial formula for Macdonald polynomials",
  "authors": [
    "Arun Ram",
    "Martha Yip"
  ],
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "In this paper we use the combinatorics of alcove walks to give a uniform combinatorial formula for Macdonald polynomials for all Lie types. These formulas are generalizations of the formulas of Haglund-Haiman-Loehr for Macdonald polynoimals of type GL(n). At q=0 these formulas specialize to the formula of Schwer for the Macdonald spherical function in terms of positively folded alcove walks and at q=t=0 these formulas specialize to the formula for the Weyl character in terms of the Littelmann path model (in the positively folded gallery form of Gaussent-Littelmann).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-05T18:01:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "33D52"
    ],
    "keywords": [
      "macdonald polynomials",
      "uniform combinatorial formula",
      "littelmann path model",
      "macdonald spherical function",
      "positively folded gallery form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.1146R"
    }
  }
}