{
  "id": "0910.5026",
  "version": "v1",
  "published": "2009-10-27T01:46:50.000Z",
  "updated": "2009-10-27T01:46:50.000Z",
  "title": "On some partitions of an affine flag variety",
  "authors": [
    "Xuhua He"
  ],
  "comment": "Preliminary version. Comments are welcome",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "In this paper, we discuss some partitions of affine flag varieties. These partitions include as special cases the partition of affine flag variety into affine Deligne-Lusztig varieties and the affine analogue of the partition of flag varieties into $\\cb_w(b)$ introduced by Lusztig in \\cite{L1} as part of the definition of character sheaves. Among other things, we give a formula for the dimension of affine Deligne-Lusztig varieties for classical loop groups in terms of degrees of class polynomials of extended affine Hecke algebra. We also prove that any simple $GL_n(\\FF_q((\\e)))$-module occurs as a subquotient of the cohomology of affine Deligne-Lusztig variety $X_w(1)$ for some $w$ in the extended affine Weyl group $\\ZZ^n \\rtimes S_n$ must occurs for some $w$ in the finite Weyl group $S_n$. Similar result holds for $Sp_{2n}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-27T01:46:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine flag variety",
      "affine deligne-lusztig variety",
      "extended affine hecke algebra",
      "extended affine weyl group",
      "finite weyl group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.5026H"
    }
  }
}