{
  "id": "2005.13484",
  "version": "v1",
  "published": "2020-05-27T16:47:11.000Z",
  "updated": "2020-05-27T16:47:11.000Z",
  "title": "The Kirillov model in families",
  "authors": [
    "Nadir Matringe",
    "Gilbert Moss"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $F$ be a non-archimedean local field, let $k$ be an algebraically closed field of characteristic $\\ell$ different from the residual characteristic of $F$, and let $A$ be a commutative Noetherian $W(k)$-algebra, where $W(k)$ denotes the Witt vectors. Using the Rankin-Selberg functional equations and extending recent results of the second author, we show that if $V$ is an $A[\\text{GL}_n(F)]$-module of Whittaker type, then the mirabolic restriction map on its Whittaker space is injective. In the special case where $A=k=\\overline{\\mathbb{F}_{\\ell}}$ and $V$ is irreducible generic, our result in particular answers a question of Vign\\'eras from 1989.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-27T16:47:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "11F70",
      "11F33"
    ],
    "keywords": [
      "kirillov model",
      "non-archimedean local field",
      "mirabolic restriction map",
      "rankin-selberg functional equations",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}