{
  "id": "2101.02063",
  "version": "v1",
  "published": "2021-01-06T14:31:05.000Z",
  "updated": "2021-01-06T14:31:05.000Z",
  "title": "Transfer of characters for discrete series representations of the unitary groups in the equal rank case via the Cauchy-Harish-Chandra integral",
  "authors": [
    "Allan Merino"
  ],
  "comment": "32 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "As conjectured by T. Przebinda, the transfer of characters in the Howe's correspondence should be obtained via the Cauchy-Harish-Chandra integral. In this paper, we prove that the conjecture holds for the dual pair $(G = U(p, q), G' = U(r, s))$, $p+q = r+s$, starting with a discrete series representation $\\Pi$ of $\\widetilde{U}(p, q)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-06T14:31:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E45",
      "22E46",
      "22E30"
    ],
    "keywords": [
      "discrete series representation",
      "equal rank case",
      "cauchy-harish-chandra integral",
      "unitary groups",
      "characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}