{
  "id": "1802.07514",
  "version": "v1",
  "published": "2018-02-21T11:09:25.000Z",
  "updated": "2018-02-21T11:09:25.000Z",
  "title": "On some properties of the functors ${\\mathcal F}^G_P$ from Lie algebra to locally analytic representations",
  "authors": [
    "Sascha Orlik",
    "Matthias Strauch"
  ],
  "comment": "36 pages",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "For a split reductive group $G$ over a finite extension $L$ of ${\\mathbb Q}_p$, and a parabolic subgroup $P \\subset G$ we examine functorial properties of the functors ${\\mathcal F}^G_P$ introduced in \\cite{OS2,OS3}. We discuss the aspects of faithfulness, projective and injective objects, Ext-groups and some kind of adjunction formulas. Here we apply the (naive) Jacquet functor and a more detailed study of the category ${\\mathcal O}^B$ introduced in \\cite{OS3}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-21T11:09:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "20G05",
      "20G25",
      "17B35",
      "11S37",
      "22E35",
      "17B15"
    ],
    "keywords": [
      "locally analytic representations",
      "lie algebra",
      "finite extension",
      "parabolic subgroup",
      "functorial properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}