{
  "id": "1811.10434",
  "version": "v1",
  "published": "2018-11-23T10:22:40.000Z",
  "updated": "2018-11-23T10:22:40.000Z",
  "title": "Linear versus spin: representation theory of the symmetric groups",
  "authors": [
    "Sho Matsumoto",
    "Piotr Śniady"
  ],
  "comment": "31 pages. arXiv admin note: text overlap with arXiv:1810.13255",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreducible spin characters evaluated on a strict partition $\\xi$ with analogous normalized linear characters evaluated on the double partition $D(\\xi)$. We also relate some natural filtration on the usual (linear) Kerov-Olshanski algebra of polynomial functions on the set of Young diagrams with its spin counterpart. Finally, we give a spin counterpart to Stanley formula for the characters of the symmetric groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-23T10:22:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C25",
      "20C30",
      "05E05"
    ],
    "keywords": [
      "symmetric groups",
      "spin counterpart",
      "normalized linear characters",
      "linear asymptotic representation theory",
      "kerov-olshanski algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}