{
  "id": "1202.5743",
  "version": "v2",
  "published": "2012-02-26T11:25:41.000Z",
  "updated": "2013-05-15T17:36:49.000Z",
  "title": "Classification of symmetric pairs with discretely decomposable restrictions of (g,K)-modules",
  "authors": [
    "Toshiyuki Kobayashi",
    "Yoshiki Oshima"
  ],
  "comment": "To appear in Crelles J. (19 pages)",
  "doi": "10.1515/crelle-2013-0045",
  "categories": [
    "math.RT"
  ],
  "abstract": "We give a complete classification of reductive symmetric pairs (g, h) with the following property: there exists at least one infinite-dimensional irreducible (g,K)-module X that is discretely decomposable as an (h,H \\cap K)-module. We investigate further if such X can be taken to be a minimal representation, a Zuckerman derived functor module A_q(\\lambda), or some other unitarizable (g,K)-module. The tensor product $\\pi_1 \\otimes \\pi_2$ of two infinite-dimensional irreducible (g,K)-modules arises as a very special case of our setting. In this case, we prove that $\\pi_1 \\otimes \\pi_2$ is discretely decomposable if and only if they are simultaneously highest weight modules.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-15T17:36:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "53C35"
    ],
    "keywords": [
      "discretely decomposable restrictions",
      "simultaneously highest weight modules",
      "zuckerman derived functor module",
      "reductive symmetric pairs",
      "infinite-dimensional irreducible"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.5743K"
    }
  }
}