{
  "id": "math/9702220",
  "version": "v1",
  "published": "1997-02-04T00:00:00.000Z",
  "updated": "1997-02-04T00:00:00.000Z",
  "title": "Prehomogeneous vector spaces and ergodic theory III",
  "authors": [
    "Akihiko Yukie"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let H_1=SL(5), H_2=SL(3), H=H_1 \\times H_2. It is known that (G,V) is a prehomogeneous vector space (see [22], [26], [25], for the definition of prehomogeneous vector spaces). A non-constant polynomial \\delta(x) on V is called a relative invariant polynomial if there exists a character \\chi such that \\delta(gx)=\\chi(g)\\delta(x). Such \\delta(x) exists for our case and is essentially unique. So we define V^{ss}={x in V such that \\delta(x) is not equal to 0}. For x in V_R^{ss}, let H_{x R+}^0 be the connected component of 1 in classical topology of the stabilizer H_{x R}. We will prove that if x in V_R^ss is \"sufficiently irrational\", H_{x R+}^0 H_Z is dense in H_R.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-02-04T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "prehomogeneous vector space",
      "ergodic theory",
      "relative invariant polynomial",
      "non-constant polynomial",
      "definition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}