{
  "id": "1909.07010",
  "version": "v1",
  "published": "2019-09-16T06:20:31.000Z",
  "updated": "2019-09-16T06:20:31.000Z",
  "title": "Cyclic sieving phenomenon on dominant maximal weights over affine Kac-Moody algebras",
  "authors": [
    "Young-Hun Kim",
    "Se-jin Oh",
    "Young-Tak Oh"
  ],
  "comment": "50 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We construct a (bi)cyclic sieving phenomenon on the union of dominant maximal weights for level $\\ell$ highest weight modules over an affine Kac-Moody algebra with exactly one highest weight being taken for each equivalence class, in a way not depending on types, ranks and levels. In order to do that, we introduce $\\textbf{\\textit{S}}$-evaluation on the set of dominant maximal weights for each highest modules, and generalize Sagan's action by considering the datum on each affine Kac-Moody algebra. As consequences, we obtain closed and recursive formulae for cardinality of the number of dominant maximal weights for every highest weight module and observe level-rank duality on the cardinalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-16T06:20:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E18",
      "05E10",
      "17B10",
      "17B67"
    ],
    "keywords": [
      "dominant maximal weights",
      "affine kac-moody algebra",
      "cyclic sieving phenomenon",
      "highest weight module",
      "equivalence class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}