{
  "id": "1612.09173",
  "version": "v1",
  "published": "2016-12-29T15:29:58.000Z",
  "updated": "2016-12-29T15:29:58.000Z",
  "title": "Zeta Functions of Lattices of the Symmetric Group",
  "authors": [
    "Tommy Hofmann"
  ],
  "journal": "Communications in Algebra Vol. 44, 2016, 2243-2255",
  "doi": "10.1080/00927872.2015.1044102",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "The symmetric group $\\mathfrak S_{n+1}$ of degree $n+1$ admits an $n$-dimensional irreducible $\\mathbf Q \\mathfrak S_n$-module $V$ corresponding to the hook partition $(2,1^{n-1})$. By the work of Craig and Plesken we know that there are $\\sigma(n+1)$ many isomorphism classes of $\\mathbf Z \\mathfrak S_{n+1}$-lattices which are rationally equivalent to $V$, where $\\sigma$ denotes the divisor counting function. In the present paper we explicitly compute the Solomon zeta function of these lattices. As an application we obtain the Solomon zeta function of the $\\mathbf Z \\mathfrak S_{n+1}$-lattice defined by the Specht basis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-29T15:29:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C10",
      "11S45"
    ],
    "keywords": [
      "symmetric group",
      "solomon zeta function",
      "divisor counting function",
      "isomorphism classes",
      "hook partition"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Taylor-Francis"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}