{
  "id": "0802.0974",
  "version": "v1",
  "published": "2008-02-07T13:38:21.000Z",
  "updated": "2008-02-07T13:38:21.000Z",
  "title": "Branching Laws for Some Unitary Representations of SL(4,R)",
  "authors": [
    "Bent Orsted",
    "Birgit Speh"
  ],
  "comment": "This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/",
  "journal": "SIGMA 4 (2008), 017, 19 pages",
  "doi": "10.3842/SIGMA.2008.017",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper we consider the restriction of a unitary irreducible representation of type $A_{\\mathfrak q}(\\lambda)$ of $GL(4,{\\mathbb R})$ to reductive subgroups $H$ which are the fixpoint sets of an involution. We obtain a formula for the restriction to the symplectic group and to $GL(2,{\\mathbb C})$, and as an application we construct in the last section some representations in the cuspidal spectrum of the symplectic and the complex general linear group. In addition to working directly with the cohmologically induced module to obtain the branching law, we also introduce the useful concept of pseudo dual pairs of subgroups in a reductive Lie group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-02-07T13:38:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "branching law",
      "unitary representations",
      "complex general linear group",
      "pseudo dual pairs",
      "restriction"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2008,
      "month": "Feb",
      "volume": 4,
      "pages": "017"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008SIGMA...4..017O"
    }
  }
}