{
  "id": "0906.2254",
  "version": "v2",
  "published": "2009-06-12T04:14:38.000Z",
  "updated": "2010-01-21T08:11:05.000Z",
  "title": "On intersections of conjugacy classes and Bruhat cells",
  "authors": [
    "Kei Yuen Chan",
    "Jiang-Hua Lu",
    "Simon Kai Ming To"
  ],
  "comment": "20 pages. Revised version. to appear in Transformation Groups",
  "categories": [
    "math.RT"
  ],
  "abstract": "For a connected complex semi-simple Lie group $G$ and a fixed pair $(B, B^-)$ of opposite Borel subgroups of $G$, we determine when the intersection of a conjugacy class $C$ in $G$ and a double coset $BwB^-$ is non-empty, where $w$ is in the Weyl group $W$ of $G$. The question comes from Poisson geometry, and our answer is in terms of the Bruhat order on $W$ and an involution $\\mc \\in W$ associated to $C$. We study properties of the elements $\\mc$. For $G = SL(n+1, \\Cset)$, we describe $\\mc$ explicitly for every conjugacy class $C$, and for the case when $w \\in W$ is an involution, we also give an explicit answer to when $C \\cap (BwB)$ is non-empty.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-01-21T08:11:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjugacy classes",
      "bruhat cells",
      "intersection",
      "connected complex semi-simple lie group",
      "opposite borel subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.2254Y"
    }
  }
}