{
  "id": "math/0211434",
  "version": "v1",
  "published": "2002-11-27T21:25:59.000Z",
  "updated": "2002-11-27T21:25:59.000Z",
  "title": "Determining whether certain affine Deligne-Lusztig sets are empty",
  "authors": [
    "Daniel C. Reuman"
  ],
  "comment": "135 pages, 112 figures",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let F be a non-archimedean local field, let L be the maximal unramified extension of F, and let fr be the Frobenius automorphism. Let G be a split connected reductive group over F, and let B(1) be the Bruhat-Tits building associated to G(F). We know that fr acts on G(L) with fixed points G(F). Let I be the Iwahori associated to a chamber in B(1). We have the relative position map, inv, from G(L)/I x G(L)/I to the extended affine Weyl group, W_e of G. If w is in W_e and b is in G(L), then the affine Deligne-Lusztig set Xw(b fr) is {x in G(L)/I : inv(x,b fr(x)) = w}. This paper answers the question of which Xw(b fr) are non-empty for certain G and b.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-11-27T21:25:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G25"
    ],
    "keywords": [
      "affine deligne-lusztig set xw",
      "extended affine weyl group",
      "non-archimedean local field",
      "relative position map",
      "maximal unramified extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 135,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....11434R"
    }
  }
}