{
  "id": "math/0410006",
  "version": "v2",
  "published": "2004-10-01T03:44:16.000Z",
  "updated": "2005-01-20T22:13:57.000Z",
  "title": "On a class of double cosets in reductive algebraic groups",
  "authors": [
    "Jiang-Hua Lu",
    "Milen Yakimov"
  ],
  "comment": "AMS-Latex, 24 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We study a class of double coset spaces R_A \\backslash G_1 \\times G_2 /R_C, where G_1 and G_2 are connected reductive algebraic groups, and R_A and R_C are certain spherical subgroups of G_1 \\times G_2 obtained by ``identifying'' Levi factors of parabolic subgroups in G_1 and G_2. Such double cosets naturally appear in the symplectic leaf decompositions of Poisson homogeneous spaces of complex reductive groups with the Belavin-Drinfeld Poisson structures. They also appear in orbit decompositions of the De Concini-Procesi compactifications of semi-simple groups of adjoint type. We find explicit parametrizations of the double coset spaces and describe the double cosets as homogeneous spaces of R_A \\times R_C. We further show that all such double cosets give rise to set-theoretical solutions to the quantum Yang-Baxter equation on unipotent algebraic groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-01-20T22:13:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reductive algebraic groups",
      "double coset spaces",
      "unipotent algebraic groups",
      "belavin-drinfeld poisson structures",
      "quantum yang-baxter equation"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10006L"
    }
  }
}