{
  "id": "0811.4152",
  "version": "v1",
  "published": "2008-11-25T18:28:50.000Z",
  "updated": "2008-11-25T18:28:50.000Z",
  "title": "Combinatorial Formulas for Macdonald and Hall-Littlewood Polynomials of Types A and C. Extended Abstract",
  "authors": [
    "Cristian Lenart"
  ],
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "A breakthrough in the theory of (type A) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of fillings of Young diagrams. Recently, Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of the corresponding affine Weyl group. In this paper, we show that a Haglund-Haiman-Loehr type formula follows naturally from the more general Ram-Yip formula, via compression. Then we extend this approach to the Hall-Littlewood polynomials of type C, which are specializations of the corresponding Macdonald polynomials at q=0. We note that no analog of the Haglund-Haiman-Loehr formula exists beyond type A, so our work is a first step towards finding such a formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-25T18:28:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05"
    ],
    "keywords": [
      "hall-littlewood polynomials",
      "combinatorial formula",
      "extended abstract",
      "corresponding affine weyl group",
      "general ram-yip formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.4152L"
    }
  }
}