{
  "id": "1303.5795",
  "version": "v1",
  "published": "2013-03-22T23:34:04.000Z",
  "updated": "2013-03-22T23:34:04.000Z",
  "title": "Geometric realization of special cases of local Langlands and Jacquet-Langlands correspondences",
  "authors": [
    "Mitya Boyarchenko",
    "Jared Weinstein"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let F be a non-Archimedean local field and let E be an unramified extension of F of degree n>1. To each sufficiently generic multiplicative character of E (the details are explained in the body of the paper) one can associate an irreducible n-dimensional representation of the Weil group W_F of F, which corresponds to an irreducible supercuspidal representation \\pi\\ of GL_n(F) via the local Langlands correspondence. In turn, via the Jacquet-Langlands correspondence, \\pi\\ corresponds to an irreducible representation \\rho\\ of the multiplicative group of the central division algebra over F with invariant 1/n. In this note we give a new geometric construction of the representations \\pi\\ and \\rho, which is simpler than the existing algebraic approaches (in particular, the use of the Weil representation over finite fields is eliminated).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-22T23:34:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "jacquet-langlands correspondence",
      "geometric realization",
      "special cases",
      "non-archimedean local field",
      "central division algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.5795B"
    }
  }
}