{
  "id": "1504.05374",
  "version": "v1",
  "published": "2015-04-21T10:22:52.000Z",
  "updated": "2015-04-21T10:22:52.000Z",
  "title": "Non-Reductive Conjugation on the Nilpotent Cone",
  "authors": [
    "Magdalena Boos"
  ],
  "comment": "The final publication is available at http://link.springer.com/article/10.1007%2Fs10468-014-9465-z",
  "journal": "Algebras and Representation Theory, Volume 17, Issue 6 , pp 1683-1706, 2014",
  "doi": "10.1007/s10468-014-9465-z",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of ${\\rm GL}_n(\\mathbf{C})$, especially of the Borel subgroup $B$ and of the standard unipotent subgroup $U$ of the latter on the nilpotent cone of complex nilpotent matrices. We obtain generic normal forms of the orbits and describe generating (semi-) invariants for the Borel semi-invariant ring as well as for the $U$-invariant ring. The latter is described in more detail in terms of algebraic quotients by a special toric variety closely related. The study of a GIT-quotient for the Borel-action is initiated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-21T10:22:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L24",
      "16W22",
      "16G20"
    ],
    "keywords": [
      "nilpotent cone",
      "non-reductive conjugation",
      "toric variety",
      "arbitrary upper-block parabolic subgroup",
      "standard unipotent subgroup"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150405374B"
    }
  }
}