{
  "id": "0906.0186",
  "version": "v1",
  "published": "2009-05-31T22:06:35.000Z",
  "updated": "2009-05-31T22:06:35.000Z",
  "title": "On Some Stratifications of Affine Deligne-Lusztig Varieties for SL_3",
  "authors": [
    "Boris Zbarsky"
  ],
  "comment": "56 pages, 2 figures",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "Let L be k((\\epsilon)), where k is an algebraic closure of a finite field with q elements and \\epsilon is an indeterminate, and let \\sigma be the Frobenius automorphism. Let G be a split connected reductive group over the fixed field of \\sigma in L, and let I be the Iwahori subgroup of G(L) associated to a given Borel subgroup of G. Let W be the extended affine Weyl group of G. Given x in W and b in G(L), we have some subgroup of G(L) that acts on the affine Deligne-Lusztig variety X_x(b) = {gI in G(L)/I : g^{-1}b\\sigma(g) is in IxI} and hence a representation of this subgroup on the Borel-Moore homology of the variety. We investigate this representation for certain b in the cases when G is SL_2 and G is SL_3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-31T22:06:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine deligne-lusztig variety",
      "stratifications",
      "extended affine weyl group",
      "borel-moore homology",
      "algebraic closure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.0186Z"
    }
  }
}