{
  "id": "1108.2007",
  "version": "v2",
  "published": "2011-08-09T18:39:41.000Z",
  "updated": "2011-12-08T04:37:44.000Z",
  "title": "Jack vertex operators and realization of Jack functions",
  "authors": [
    "Wuxing Cai",
    "Naihuan Jing"
  ],
  "comment": "Expanded version",
  "journal": "J. Algebr. Comb. 39 (2014), 53--74",
  "doi": "10.1007/s10801-013-0438-9",
  "categories": [
    "math.CO",
    "math.QA"
  ],
  "abstract": "We give an iterative method to realize general Jack functions from Jack functions of rectangular shapes. We first show some cases of Stanley's conjecture on positivity of the Littlewood-Richardson coefficients, and then use this method to give a new realization of Jack functions. We also show in general that vectors of products of Jack vertex operators form a basis of symmetric functions. In particular this gives a new proof of linear independence for the rectangular and marked rectangular Jack vertex operators. Thirdly a generalized Frobenius formula for Jack functions was given and was used to give new evaluation of Dyson integrals and even powers of Vandermonde determinant.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-08T04:37:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "17B69",
      "05E10"
    ],
    "keywords": [
      "realization",
      "marked rectangular jack vertex operators",
      "jack vertex operators form",
      "realize general jack functions",
      "littlewood-richardson coefficients"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.2007C"
    }
  }
}