{
  "id": "1009.4051",
  "version": "v3",
  "published": "2010-09-21T10:52:14.000Z",
  "updated": "2012-05-21T16:30:25.000Z",
  "title": "Quotients by actions of the derived group of a maximal unipotent subgroup",
  "authors": [
    "Dmitri I. Panyushev"
  ],
  "comment": "23 pages, final version, to appear in Pacific J Math",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $U$ be a maximal unipotent subgroup of a connected semisimple group $G$ and $U'$ the derived group of $U$. If $X$ is an affine $G$-variety, then the algebra of $U'$-invariants, $k[X]^U'$, is finitely generated and the quotient morphism $\\pi: X \\to X//U'$ is well-defined. In this article, we study properties of such quotient morphisms, e.g. the property that all the fibres of $\\pi$ are equidimensional. We also establish an analogue of the Hilbert-Mumford criterion for the null-cones with respect to $U'$-invariants.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-05-21T16:30:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "17B20",
      "22E46"
    ],
    "keywords": [
      "maximal unipotent subgroup",
      "derived group",
      "quotient morphism",
      "invariants",
      "hilbert-mumford criterion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.4051P"
    }
  }
}