{
  "id": "1606.08840",
  "version": "v1",
  "published": "2016-06-28T19:54:40.000Z",
  "updated": "2016-06-28T19:54:40.000Z",
  "title": "Parabolic Conjugation and Commuting Varieties",
  "authors": [
    "Magdalena Boos",
    "Michaël Bulois"
  ],
  "comment": "Comments welcome",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of the general linear group on the variety of nilpotent matrices in its Lie algebra. Lie-theoretically, it is natural to wonder about the number of orbits of this action. We translate the setup to a representation-theoretic one and obtain a finiteness criterion which classifies all actions with only a finite number of orbits over an arbitrary infinite field. These results are applied to commuting varieties and nested punctual Hilbert schemes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-28T19:54:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "14R20",
      "14C05",
      "17B08"
    ],
    "keywords": [
      "commuting varieties",
      "parabolic conjugation",
      "arbitrary upper-block parabolic subgroup",
      "arbitrary infinite field",
      "nested punctual hilbert schemes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}