{
  "id": "2003.10700",
  "version": "v1",
  "published": "2020-03-24T07:43:22.000Z",
  "updated": "2020-03-24T07:43:22.000Z",
  "title": "The plethystic inverse of the odd Lie representations $Lie_{2n+1}$",
  "authors": [
    "Sheila Sundaram"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "The Frobenius characteristic of $Lie_n,$ the representation of the symmetric group $S_n$ afforded by the free Lie algebra, is known to satisfy many interesting plethystic identities. In this paper we prove a conjecture of Richard Stanley establishing the plethystic inverse of the sum $\\sum_{n\\geq 0} Lie_{2n+1}$ of the odd Lie characteristics. We obtain an apparently new plethystic decomposition of the regular representation of $S_n$ in terms of irreducibles indexed by hooks, and the Lie representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-24T07:43:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "20C30"
    ],
    "keywords": [
      "odd lie representations",
      "plethystic inverse",
      "free lie algebra",
      "odd lie characteristics",
      "frobenius characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}