{
  "id": "1510.06213",
  "version": "v1",
  "published": "2015-10-21T11:27:34.000Z",
  "updated": "2015-10-21T11:27:34.000Z",
  "title": "Shalika periods and parabolic induction for GL(n) over a non archimedean local field",
  "authors": [
    "Nadir Matringe"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $F$ be a non archimedean local field, and $n_1$ and $n_2$ two positive even integers. We prove that if $\\pi_1$ and $\\pi_2$ are two smooth representations of $GL(n_1,F)$ and $GL(n_2,F)$ respectively, both admitting a Shalika period, then the normalised parabolically induced representation $\\pi_1\\times \\pi_2$ also admits a Shalika period. Combining this with the results of \\cite{M-localBF}, we obtain as a corollary the classification of generic representations of $GL(n,F)$ admitting a Shalika period when $F$ has characteristic zero. This result is relevant to the study of the Jacquet-Shalika exterior square $L$ factor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-21T11:27:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50"
    ],
    "keywords": [
      "non archimedean local field",
      "shalika period",
      "parabolic induction",
      "jacquet-shalika exterior square",
      "smooth representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151006213M"
    }
  }
}