{
  "id": "2407.01766",
  "version": "v1",
  "published": "2024-07-01T19:58:15.000Z",
  "updated": "2024-07-01T19:58:15.000Z",
  "title": "Irreducible smooth representations in defining characteristic without central character",
  "authors": [
    "Daniel Le"
  ],
  "comment": "5 pages",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "Let $p>3$ and $F$ be a non-archimedean local field with residue field a proper finite extension of $\\mathbb{F}_p$. Let $E$ be an algebraically closed countable field extension of the residue field of $F$. In this short note, we explain how the methods from arXiv:1809.10247 and arXiv:2210.07281 can be used to construct irreducible smooth representations of $\\mathrm{GL}_n(F)$, $n>1$, over $E$ without a central character.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-01T19:58:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50"
    ],
    "keywords": [
      "central character",
      "defining characteristic",
      "closed countable field extension",
      "residue field",
      "non-archimedean local field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}