{
  "id": "1009.4486",
  "version": "v1",
  "published": "2010-09-22T21:36:40.000Z",
  "updated": "2010-09-22T21:36:40.000Z",
  "title": "A generalized Macdonald operator",
  "authors": [
    "J. F. van Diejen",
    "E. Emsiz"
  ],
  "comment": "11 pages. To appear in Int. Math. Res. Not. IMRN",
  "journal": "International Mathematics Research Notices, Vol. 2011, No. 15, pp. 3560-3574",
  "doi": "10.1093/imrn/rnq233",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We present an explicit difference operator diagonalized by the Macdonald polynomials associated with an (arbitrary) admissible pair of irreducible reduced crystallographic root systems. By the duality symmetry, this gives rise to an explicit Pieri formula for the Macdonald polynomials in question. The simplest examples of our construction recover Macdonald's celebrated difference operators and associated Pieri formulas pertaining to the minuscule and quasi-minuscule weights. As further by-products, explicit expansions and Littlewood-Richardson type formulas are obtained for the Macdonald polynomials associated with a special class of small weights.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-22T21:36:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D52",
      "05E05",
      "17B20",
      "20F55"
    ],
    "keywords": [
      "generalized macdonald operator",
      "macdonald polynomials",
      "irreducible reduced crystallographic root systems",
      "explicit difference operator",
      "littlewood-richardson type formulas"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.4486V"
    }
  }
}