{
  "id": "1104.0705",
  "version": "v2",
  "published": "2011-04-04T22:35:49.000Z",
  "updated": "2016-04-24T20:48:16.000Z",
  "title": "Irreducible characters of GSp(4, q) and dimensions of spaces of fixed vectors",
  "authors": [
    "Jeffery Breeding II"
  ],
  "comment": "48 pages, 21 tables. Corrected an error in Table 16 for type V* representations (theta_11 and theta_12 were switched)",
  "journal": "Ramanujan J. 36 (2015), no. 3, 305-354",
  "doi": "10.1007/s11139-014-9622-3",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "In this paper, we compute the conjugacy classes and the list of irreducible characters of GSp(4,q), where q is odd. We also determine precisely which irreducible characters are non-cuspidal and which are generic. These characters are then used to compute dimensions of certain subspaces of fixed vectors of smooth admissible non-supercuspidal representations of GSp(4,F), where F is a non-archimedean local field of characteristic zero with residue field of order q.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-04T22:35:49.000Z",
      "title": "Irreducible characters of GSp(4, Fq)",
      "abstract": "Admissible non-supercuspidal representations of GSp(4,F), where F is a local field of characteristic zero with an odd-ordered residue field Fq, have finite dimensional spaces of fixed vectors under the action of principal congruence subgroups. We can say precisely what these dimensions are for nearly all local fields and principal congruence subgroups of level p by understanding the non-cuspidal representation theory of the finite group GSp(4,Fq). The conjugacy classes and the list of irreducible characters of this group are given. Genericity and cuspidality of the irreducible characters are also determined.",
      "comment": "30 pages, 11 tables, results of author's thesis",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-04-24T20:48:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F46",
      "11F70",
      "11F85"
    ],
    "keywords": [
      "irreducible characters",
      "principal congruence subgroups",
      "local field",
      "non-cuspidal representation theory",
      "finite dimensional spaces"
    ],
    "tags": [
      "dissertation",
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.0705B"
    }
  }
}