{
  "id": "1408.3679",
  "version": "v1",
  "published": "2014-08-15T23:41:25.000Z",
  "updated": "2014-08-15T23:41:25.000Z",
  "title": "Resolutions for principal series representations of p-adic GL(n)",
  "authors": [
    "Rachel Ollivier"
  ],
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "Let F be a nonarchimedean locally compact field with residue characteristic p and G(F) the group of F-rational points of a connected reductive group. Following Schneider and Stuhler, one can realize, in a functorial way, any smooth complex finitely generated representation of G(F) as the 0-homology of a certain coefficient system on the semi-simple building of G(F). It is known that this method does not apply in general for smooth mod p representations of G(F), even when G= GL(2). However, we prove that a principal series representation of GL(n,F) over a field with arbitrary characteristic can be realized as the 0-homology of the corresponding coefficient system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-15T23:41:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "principal series representation",
      "p-adic gl",
      "resolutions",
      "nonarchimedean locally compact field",
      "smooth complex finitely generated representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.3679O"
    }
  }
}