{
  "id": "math/0303146",
  "version": "v1",
  "published": "2003-03-12T16:27:30.000Z",
  "updated": "2003-03-12T16:27:30.000Z",
  "title": "Formulas for the dimensions of some affine Deligne-Lusztig Varieties",
  "authors": [
    "Daniel C. Reuman"
  ],
  "comment": "16 pages, 10 figures",
  "journal": "Michigan Math. J. 52 (2004), 435-451",
  "categories": [
    "math.RT"
  ],
  "abstract": "Rapoport and Kottwitz defined the affine Deligne-Lusztig varieties $X_{\\tilde{w}}^P(b\\sigma)$ of a quasisplit connected reductive group $G$ over $F = \\mathbb{F}_q((t))$ for a parahoric subgroup $P$. They asked which pairs $(b, \\tilde{w})$ give non-empty varieties, and in these cases what dimensions do these varieties have. This paper answers these questions for $P=I$ an Iwahori subgroup, in the cases $b=1$, $G=SL_2$, $SL_3$, $Sp_4$. This information is used to get a formula for the dimensions of the $X_{\\tilde{w}}^K(\\sigma)$ (all shown to be non-empty by Rapoport and Kottwitz) for the above $G$ that supports a general conjecture of Rapoport. Here $K$ is a special maximal compact subgroup.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-03-12T16:27:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G25"
    ],
    "keywords": [
      "affine deligne-lusztig varieties",
      "dimensions",
      "special maximal compact subgroup",
      "parahoric subgroup",
      "quasisplit connected reductive group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......3146R"
    }
  }
}