{
  "id": "0806.3063",
  "version": "v1",
  "published": "2008-06-18T18:38:05.000Z",
  "updated": "2008-06-18T18:38:05.000Z",
  "title": "Berezin-Toeplitz quantization on Lie groups",
  "authors": [
    "Brian C. Hall"
  ],
  "comment": "To appear in Journal of Functional Analysis",
  "journal": "Journal of Functional Analysis, Vol. 255 (2008), 2488-2506",
  "doi": "10.1016/j.jfa.2008.06.022",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let K be a connected compact semisimple Lie group and Kc its complexification. The generalized Segal-Bargmann space for Kc, is a space of square-integrable holomorphic functions on Kc, with respect to a K-invariant heat kernel measure. This space is connected to the \"Schrodinger\" Hilbert space L^2(K) by a unitary map, the generalized Segal-Bargmann transform. This paper considers certain natural operators on L^2(K), namely multiplication operators and differential operators, conjugated by the generalized Segal-Bargmann transform. The main results show that the resulting operators on the generalized Segal-Bargmann space can be represented as Toeplitz operators. The symbols of these Toeplitz operators are expressed in terms of a certain subelliptic heat kernel on Kc. I also examine some of the results from an infinite-dimensional point of view based on the work of L. Gross and P. Malliavin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-18T18:38:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81S10",
      "22E30"
    ],
    "keywords": [
      "berezin-toeplitz quantization",
      "generalized segal-bargmann transform",
      "generalized segal-bargmann space",
      "toeplitz operators",
      "connected compact semisimple lie group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.3063H"
    }
  }
}