{
  "id": "math/9708209",
  "version": "v1",
  "published": "1997-08-28T00:00:00.000Z",
  "updated": "1997-08-28T00:00:00.000Z",
  "title": "A remark on the regularity of prehomogeneous vector spaces",
  "authors": [
    "Akihiko Yukie"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In this note, we prove that if $(G,V)$ is a prehomogeneous vector space over any field $k$ such that the stabilizer of a generic point is reductive, the set of semi-stable points is a single orbit over the separable closure of $k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-08-28T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "prehomogeneous vector space",
      "regularity",
      "generic point",
      "single orbit",
      "semi-stable points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}