{
  "id": "1805.02040",
  "version": "v1",
  "published": "2018-05-05T10:59:13.000Z",
  "updated": "2018-05-05T10:59:13.000Z",
  "title": "Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, II: Groups of type F, G, and H",
  "authors": [
    "Paula Macedo Lins de Araujo"
  ],
  "comment": "28 pages. The paper arXiv:1802.04440v1 was split up in two. This version is the updated second part of arXiv:1802.04440v1 and companion to the recent version arXiv:1802.04440",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "This is the second of two papers introducing and investigating two bivariate zeta functions associated to unipotent group schemes over rings of integers of number fields. In the first part, we proved some of their properties such as rationality and functional equations. Here, we calculate such bivariate zeta functions of three infinite families of nilpotent groups of class 2 generalising the Heisenberg group of three by three unitriangular matrices over rings of integers of number fields. The local factors of these zeta functions are also expressed in terms of sums over finite hyperoctahedral groups, which provides formulae for joint distributions of three statistics on such groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-05T10:59:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M32",
      "20D15",
      "22E55",
      "20E45",
      "05A15",
      "05E15"
    ],
    "keywords": [
      "conjugacy class zeta functions",
      "unipotent group schemes",
      "bivariate representation",
      "bivariate zeta functions",
      "number fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}