{
  "id": "math/0607002",
  "version": "v1",
  "published": "2006-06-30T22:27:19.000Z",
  "updated": "2006-06-30T22:27:19.000Z",
  "title": "Multiplicity-free theorems of the restrictions of unitary highest weight modules with respect to reductive symmetric pairs",
  "authors": [
    "Toshiyuki Kobayashi"
  ],
  "journal": "Progr. Math., 255 (2007), pages 45-109",
  "doi": "10.1007/978-0-8176-4646-2_3",
  "categories": [
    "math.RT",
    "math.DG"
  ],
  "abstract": "The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branching theorems that include the multiplicity-free property of some of known results such as the Clebsh--Gordan--Pieri formula for tensor products, the Plancherel theorem for Hermitian symmetric spaces (also for line bundle cases), the Hua--Kostant--Schmid $K$-type formula, and the canonical representations in the sense of Vershik--Gelfand--Graev. Our method works in a uniform manner for both finite and infinite dimensional cases, for both discrete and continuous spectra, and for both classical and exceptional cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-30T22:27:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46"
    ],
    "keywords": [
      "unitary highest weight modules",
      "reductive symmetric pairs",
      "multiplicity-free theorems",
      "restrictions",
      "restricting highest weight modules"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7002K"
    }
  }
}