{
  "id": "math/0412302",
  "version": "v3",
  "published": "2004-12-15T16:11:51.000Z",
  "updated": "2006-02-01T15:46:50.000Z",
  "title": "The $G$-stable pieces of the wonderful compactification",
  "authors": [
    "Xuhua He"
  ],
  "comment": "22 pages. Some corrections. Final version",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a connected, simple algebraic group over an algebraically closed field. There is a partition of the wonderful compactification $\\bar{G}$ of $G$ into finite many $G$-stable pieces, which were introduced by Lusztig. In this paper, we will investigate the closure of any $G$-stable piece in $\\bar{G}$. We will show that the closure is a disjoint union of some $G$-stable pieces, which was first conjectured by Lusztig. We will also prove the existence of cellular decomposition if the closure contains finitely many $G$-orbits.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-02-01T15:46:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G15"
    ],
    "keywords": [
      "stable piece",
      "wonderful compactification",
      "simple algebraic group",
      "disjoint union",
      "cellular decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12302H"
    }
  }
}