{
  "id": "1006.2291",
  "version": "v1",
  "published": "2010-06-11T13:15:09.000Z",
  "updated": "2010-06-11T13:15:09.000Z",
  "title": "Dimensions of affine Deligne-Lusztig varieties in affine flag varieties",
  "authors": [
    "Ulrich Goertz",
    "Xuhua He"
  ],
  "comment": "22 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Affine Deligne-Lusztig varieties are analogs of Deligne-Lusztig varieties in the context of an affine root system. We prove a conjecture stated in the paper arXiv:0805.0045v4 by Haines, Kottwitz, Reuman, and the first named author, about the question which affine Deligne-Lusztig varieties (for a split group and a basic $\\sigma$-conjugacy class) in the Iwahori case are non-empty. If the underlying algebraic group is a classical group and the chosen basic $\\sigma$-conjugacy class is the class of $b=1$, we also prove the dimension formula predicted in op. cit. in almost all cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-11T13:15:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "20G25"
    ],
    "keywords": [
      "affine deligne-lusztig varieties",
      "affine flag varieties",
      "conjugacy class",
      "affine root system",
      "dimension formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.2291G"
    }
  }
}