{
  "id": "2303.09605",
  "version": "v1",
  "published": "2023-03-16T19:23:00.000Z",
  "updated": "2023-03-16T19:23:00.000Z",
  "title": "A cyclic sieving phenomenon for symplectic tableaux",
  "authors": [
    "Graeme Henrickson",
    "Anna Stokke",
    "Max Wiebe"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a cyclic sieving phenomenon for symplectic $\\lambda$-tableaux, $SP(\\lambda, 2m)$, where $\\lambda$ is a partition of an odd positive integer $n$ and $gcd(m,p)=1$ for any odd prime $p\\leq n$. We use the crystal structure on Kashiwara-Nakashima symplectic tableaux to get a cyclic sieving action as the product of simple reflections in the Weyl group. The cyclic sieving polynomial is the $q$-anologue of the hook-content formula for symplectic tableaux.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-16T19:23:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E18",
      "05E05",
      "05E10"
    ],
    "keywords": [
      "cyclic sieving phenomenon",
      "kashiwara-nakashima symplectic tableaux",
      "hook-content formula",
      "crystal structure",
      "odd positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}