{
  "id": "math/0106079",
  "version": "v2",
  "published": "2001-06-11T12:31:58.000Z",
  "updated": "2003-01-14T00:54:15.000Z",
  "title": "Combinatorics and invariant differential operators on multiplicity free spaces",
  "authors": [
    "Friedrich Knop"
  ],
  "comment": "36 pages, some typos corrected",
  "journal": "J. Algebra 260 (2003), 194-229",
  "doi": "10.1016/S0021-8693(02)00633-6",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We study the generalization of shifted Jack polynomials to arbitrary multiplicity free spaces. In a previous paper (math.RT/0006004) we showed that these polynomials are eigenfunctions for commuting difference operators. Our central result now is the \"transposition formula\", a generalization of Okounkov's binomial theorem (q-alg/9608021) for shifted Jack polynomials. From this formula, we derive an interpolation formula, an evaluation formula, a scalar product, a binomial theorem, and properties of the algebra generated by the multiplication and difference operators.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-01-14T00:54:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E35",
      "33C52",
      "39A70"
    ],
    "keywords": [
      "invariant differential operators",
      "shifted jack polynomials",
      "combinatorics",
      "difference operators",
      "arbitrary multiplicity free spaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......6079K"
    }
  }
}