{
  "annotation_id": "aa6d9c22-95a8-4979-b12b-a024a85d1e6d",
  "date_created": "2026-03-02T18:01:42.254000Z",
  "date_modified": "2026-03-02T18:01:42.254000Z",
  "file_hash": "58b97ccf15f6a214756b2aa40d3bc7ef122083cb389ddc1bceb367468db7f3fc",
  "private": false,
  "record": {
    "abstract": "Let K be a connected Lie group of compact type and let T*(K) be its cotangent\nbundle. This paper considers geometric quantization of T*(K), first using the\nvertical polarization and then using a natural Kahler polarization obtained by\nidentifying T*(K) with the complexified group K_C. The first main result is\nthat the Hilbert space obtained by using the Kahler polarization is naturally\nidentifiable with the generalized Segal-Bargmann space introduced by the author\nfrom a different point of view, namely that of heat kernels. The second main\nresult is that the pairing map of geometric quantization coincides with the\ngeneralized Segal-Bargmann transform introduced by the author. This means that\nin this case the pairing map is a constant multiple of a unitary map. For both\nresults it is essential that the half-form correction be included when using\nthe Kahler polarization. Together with results of the author with B. Driver,\nthese results may be seen as an instance of \"quantization commuting with\nreduction.\"",
    "arxiv_id": "quant-ph/0012105",
    "authors": [
      "Brian C. Hall"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1007/s002200200607",
    "journal_ref": "Comm. Math. Phys. Vol. 226 (2002), pp. 233-268",
    "title": "Geometric quantization and the generalized Segal-Bargmann transform for   Lie groups of compact type",
    "url": "https://arxiv.org/abs/quant-ph/0012105"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5001b76e-94a8-42d6-8f94-c10e5683c299",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}