{
  "id": "1703.09475",
  "version": "v1",
  "published": "2017-03-28T09:28:55.000Z",
  "updated": "2017-03-28T09:28:55.000Z",
  "title": "Some results on reducibility of parabolic induction for classical groups",
  "authors": [
    "Erez Lapid",
    "Marko Tadić"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Given a (complex, smooth) irreducible representation $\\pi$ of the general linear group over a non-archimedean local field and an irreducible supercuspidal representation $\\sigma$ of a classical group, we show that the (normalized) parabolic induction $\\pi\\rtimes\\sigma$ is reducible if there exists $\\rho$ in the supercuspidal support of $\\pi$ such that $\\rho\\rtimes\\sigma$ is reducible. In special cases we also give irreducibility criteria for $\\pi\\rtimes\\sigma$ when the above condition is not satisfied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-28T09:28:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parabolic induction",
      "classical group",
      "non-archimedean local field",
      "general linear group",
      "irreducible supercuspidal representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}