{
  "id": "1412.5270",
  "version": "v1",
  "published": "2014-12-17T06:44:44.000Z",
  "updated": "2014-12-17T06:44:44.000Z",
  "title": "Category ${\\mathcal O}$ and locally analytic representations",
  "authors": [
    "Sascha Orlik",
    "Matthias Strauch"
  ],
  "comment": "This article draws heavily from arXiv:1001.0323. In order to facilitate the reading of the current paper, especially the technical sections (where it deviates slightly from the previous article), we have found it useful to repeat many of the arguments from arXiv:1001.0323 in full",
  "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 introduce a category ${\\mathcal O}^P$ which is equipped with a forgetful functor to the parabolic category ${\\mathcal O}^{\\mathfrak p}$ of Bernstein, Gelfand and Gelfand. There is a canonical fully faithful embedding of a subcategory ${\\mathcal O}^{\\mathfrak p}_{\\rm alg}$ of ${\\mathcal O}^{\\mathfrak p}$ into ${\\mathcal O}^P$, which 'splits' the forgetful map. We then introduce functors from the category ${\\mathcal O}^P$ to the category of locally analytic representations, thereby generalizing the authors' previous work where these functors had been defined on the category ${\\mathcal O}^{\\mathfrak p}_{\\rm alg}$. It is shown that these functors are exact, and a criterion for the irreducibility of a representation in the image of this functor is proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-17T06:44:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "20G05",
      "20G25",
      "17B35",
      "11S37",
      "22E35",
      "17B15"
    ],
    "keywords": [
      "locally analytic representations",
      "finite extension",
      "split reductive group",
      "parabolic subgroup",
      "parabolic category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}