{
  "id": "1408.5747",
  "version": "v1",
  "published": "2014-08-25T13:21:40.000Z",
  "updated": "2014-08-25T13:21:40.000Z",
  "title": "Morita's Theory for the Symplectic Groups",
  "authors": [
    "Zhi Qi",
    "Chang Yang"
  ],
  "comment": "23 pages",
  "journal": "Int. J. Number Theory 7 (2011), no. 8, 2115-2137",
  "doi": "10.1142/S1793042111004952",
  "categories": [
    "math.RT"
  ],
  "abstract": "We construct and study the holomorphic discrete series representations and the principal series representations of the symplectic group $\\mathrm{Sp}(2n,F)$ over a $p$-adic field $F$ as well as a duality between some sub-representations of these two representations. The constructions of these two representations generalize those defined in Morita and Murase's works. Moreover, Morita built a duality for $\\mathrm{SL}(2, F)$ defined by residues. We view the duality we defined as an algebraic interpretation of Morita's duality in some extent and its generalization to the symplectic groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-25T13:21:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symplectic group",
      "moritas theory",
      "holomorphic discrete series representations",
      "principal series representations",
      "adic field"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.5747Q"
    }
  }
}