{
  "id": "1712.02416",
  "version": "v1",
  "published": "2017-12-06T21:42:23.000Z",
  "updated": "2017-12-06T21:42:23.000Z",
  "title": "Pieri rules for the Jack polynomials in superspace and the 6-vertex model",
  "authors": [
    "J. Gatica",
    "M. Jones",
    "L. Lapointe"
  ],
  "comment": "28 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We present Pieri rules for the Jack polynomials in superspace. The coefficients in the Pieri rules are, except for an extra determinant, products of quotients of linear factors in $\\alpha$ (expressed, as in the usual Jack polynomial case, in terms of certain hook-lengths in a Ferrers' diagram). We show that, surprisingly, the extra determinant is related to the partition function of the 6-vertex model. We give, as a conjecture, the Pieri rules for the Macdonald polynomials in superspace.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-06T21:42:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "82B23"
    ],
    "keywords": [
      "pieri rules",
      "superspace",
      "extra determinant",
      "usual jack polynomial case",
      "macdonald polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}