{
  "id": "1802.07352",
  "version": "v1",
  "published": "2018-02-20T21:57:17.000Z",
  "updated": "2018-02-20T21:57:17.000Z",
  "title": "Crystal graphs for shifted tableaux",
  "authors": [
    "Sami Assaf",
    "Ezgi Kantarcı Oğuz"
  ],
  "comment": "12 pages, 11 figures, to appear in FPSAC 2018 conference proceedings",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We define crystal operators on semistandard shifted tableaux, giving a new proof that Schur $P$-functions are Schur positive. We define a queer crystal operator to construct a connected queer crystal on semistandard shifted tableaux of a given shape, providing a new proof that products of Schur $P$-functions are Schur $P$-positive. We also give a rectification map from shifted tableaux to Young tableaux that commutes with the crystal operators and provides a dual algorithm to shifted insertion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-20T21:57:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "crystal graphs",
      "semistandard shifted tableaux",
      "define crystal operators",
      "queer crystal operator",
      "connected queer crystal"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}