{
  "id": "2407.06873",
  "version": "v1",
  "published": "2024-07-09T14:02:22.000Z",
  "updated": "2024-07-09T14:02:22.000Z",
  "title": "The Functors $\\mathcal{F}^G_P$ over Local Fields of Positive Characteristic",
  "authors": [
    "Georg Linden"
  ],
  "comment": "34 pages. Partially based on the author's PhD thesis arXiv:2304.03166v1. Comments welcome!",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "Let $G$ be a split connected reductive group over a non-archimedean local field. In the $p$-adic setting, Orlik-Strauch constructed functors from the BGG category $\\mathcal{O}$ associated to the Lie algebra of $G$ to the category of locally analytic representation of $G$. We generalize these functors to such groups over non-archimedean local fields of arbitrary characteristic. To this end, we introduce the hyperalgebra of a non-archimedean Lie group $G$, which generalizes its Lie algebra, and consider topological modules over the algebra of locally analytic distributions on $G$ and subalgebras related to this hyperalgebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-09T14:02:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "20G25",
      "22E35"
    ],
    "keywords": [
      "positive characteristic",
      "non-archimedean local field",
      "lie algebra",
      "non-archimedean lie group",
      "orlik-strauch constructed functors"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}