{
  "id": "1201.3646",
  "version": "v3",
  "published": "2012-01-17T21:54:44.000Z",
  "updated": "2012-10-01T20:34:18.000Z",
  "title": "Locally analytic representations and sheaves on the Bruhat-Tits building",
  "authors": [
    "Deepam Patel",
    "Tobias Schmidt",
    "Matthias Strauch"
  ],
  "comment": "Replaces earlier version. Exposition shortened and improved in several places, and new material and examples added. In particular, section 11 is new.\"",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "Let L be a finite field extension of Q_p and let G be the group of L-rational points of a split connected reductive group over L. We view G as a locally L-analytic group with Lie algebra g. We define a functor from admissible locally analytic G-representations with prescribed infinitesimal character to a category of equivariant sheaves on the Bruhat-Tits building of G. For smooth representations, the corresponding sheaves are closely related to the sheaves constructed by S. Schneider and U. Stuhler. The functor is also compatible, in a certain sense, with the localization of g-modules on the flag variety by A. Beilinson and J. Bernstein.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-10-01T20:34:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "22E50"
    ],
    "keywords": [
      "locally analytic representations",
      "bruhat-tits building",
      "finite field extension",
      "lie algebra",
      "smooth representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.3646P"
    }
  }
}