{
  "id": "1106.3296",
  "version": "v1",
  "published": "2011-06-16T18:19:25.000Z",
  "updated": "2011-06-16T18:19:25.000Z",
  "title": "From Macdonald Polynomials to a Charge Statistic beyond Type A",
  "authors": [
    "Cristian Lenart"
  ],
  "comment": "32 pages, 6 figures",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "The charge is an intricate statistic on words, due to Lascoux and Schutzenberger, which gives positive combinatorial formulas for Lusztig's q-analogue of weight multiplicities and the energy function on affine crystals, both of type A. As these concepts are defined for all Lie types, it has been a long-standing problem to express them based on a generalization of charge. I present a method for addressing this problem in classical Lie types, based on the recent Ram-Yip formula for Macdonald polynomials and the quantum Bruhat order on the corresponding Weyl group. The details of the method are carried out in type A (where we recover the classical charge) and type C (where we define a new statistic).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-16T18:19:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "33D52",
      "20G42"
    ],
    "keywords": [
      "macdonald polynomials",
      "charge statistic",
      "quantum bruhat order",
      "corresponding weyl group",
      "positive combinatorial formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.3296L"
    }
  }
}