{
  "id": "1910.02756",
  "version": "v1",
  "published": "2019-10-07T12:44:24.000Z",
  "updated": "2019-10-07T12:44:24.000Z",
  "title": "Transfer of characters in the theta correspondence with one compact member",
  "authors": [
    "Allan Merino"
  ],
  "comment": "29 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "For an irreducible dual pair $(G, G') \\in Sp(W)$ with one member compact and two representations $\\Pi \\leftrightarrow \\Pi'$ appearing in the Howe duality, we give an expression of the character $\\Theta_{\\Pi'}$ of $\\Pi'$ via the character of $\\Pi$. We make computations for the dual pair $(G = U(n, \\mathbb{C}), G' = U(p, q, \\mathbb{C}))$, which are explicit in low dimensions. For $(G = U(1, \\mathbb{C}), G' = U(1, 1, \\mathbb{C}))$, we verify directly a result of H. Hecht saying that the character has the same value on both Cartan subgroups of $G'$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-07T12:44:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E45",
      "22E46",
      "22E30"
    ],
    "keywords": [
      "theta correspondence",
      "compact member",
      "howe duality",
      "member compact",
      "low dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}