{
  "id": "math/0501057",
  "version": "v1",
  "published": "2005-01-05T07:14:34.000Z",
  "updated": "2005-01-05T07:14:34.000Z",
  "title": "Geometric representation theory for unitary groups of operator algebras",
  "authors": [
    "Daniel Beltiţ\\ua",
    "Tudor S. Ratiu"
  ],
  "comment": "17 pages",
  "categories": [
    "math.RT",
    "math.OA"
  ],
  "abstract": "Geometric realizations for the restrictions of GNS representations to unitary groups of $C^*$-algebras are constructed. These geometric realizations use an appropriate concept of reproducing kernels on vector bundles. To build such realizations in spaces of holomorphic sections, a class of complex coadjoint orbits of the corresponding real Banach-Lie groups are described and some homogeneous holomorphic Hermitian vector bundles that are naturally associated with the coadjoint orbits are constructed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-05T07:14:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "46L30",
      "22E46",
      "58B12",
      "46E22"
    ],
    "keywords": [
      "geometric representation theory",
      "unitary groups",
      "operator algebras",
      "geometric realizations",
      "homogeneous holomorphic hermitian vector bundles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1057B"
    }
  }
}