{
  "id": "1307.0606",
  "version": "v1",
  "published": "2013-07-02T07:46:13.000Z",
  "updated": "2013-07-02T07:46:13.000Z",
  "title": "Stability of Branching Laws for Highest Weight Modules",
  "authors": [
    "Masatoshi Kitagawa"
  ],
  "comment": "34 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We say a representation V of a group G has stability if its multiplicities m^{G}_{V}(\\lambda) is dependent only on some equivalence class of \\lambda for a sufficiently large parameter \\lambda. In this paper, we prove that the restriction of a holomorphic discrete series representation with respect to any holomorphic symmetric pairs has stability. As a corollary, we give a necessary and sufficient condition on multiplicity-freeness of the branching laws in this setting. This condition is same as the sufficient condition given by the theory of visible actions. We prove a general theorem before we show the stability of holomorphic discrete series representations. Using the general theorem, we also show the stability on quasi-affine spherical homogeneous spaces and the stability of K-type of unitary highest weight modules. We also show that two branching laws of a holomorphic discrete series representation coincide if two subgroups are in same \\epsilon-family.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-02T07:46:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "20G05",
      "32M15",
      "57S20"
    ],
    "keywords": [
      "branching laws",
      "holomorphic discrete series representation coincide",
      "unitary highest weight modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.0606K"
    }
  }
}