{
  "id": "1708.00383",
  "version": "v1",
  "published": "2017-08-01T15:14:18.000Z",
  "updated": "2017-08-01T15:14:18.000Z",
  "title": "Unitary representations with Dirac cohomology: finiteness in the real case",
  "authors": [
    "Chao-Ping Dong"
  ],
  "comment": "8 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a complex connected simple algebraic group with a fixed real form $\\sigma$. Let $G(\\mathbb{R})=G^\\sigma$ be the corresponding group of real points. Let $\\theta$ be the Cartan involution of $G$ corresponding to $\\sigma$. This paper shows that, up to equivalence, for all but finitely many exceptions, any irreducible unitary Harish-Chandra module $\\pi$ of $G(\\mathbb{R})$ having non-zero Dirac cohomology must be cohomologically induced from an irreducible unitary Harish-Chandra module $\\pi_{L(\\mathbb{R})}$ of $L(\\mathbb{R})$ with nonvanishing Dirac cohomology. Moreover, $\\pi_{L(\\mathbb{R})}$ is in the good range. Here $L(\\mathbb{R})$ is a proper $\\theta$-stable Levi subgroup of $G(\\mathbb{R})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-01T15:14:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unitary representations",
      "real case",
      "irreducible unitary harish-chandra module",
      "finiteness",
      "complex connected simple algebraic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}