{
  "id": "0809.0245",
  "version": "v1",
  "published": "2008-09-01T13:50:26.000Z",
  "updated": "2008-09-01T13:50:26.000Z",
  "title": "Ideals in Parabolic Subalgebras of Simple Lie Algebras",
  "authors": [
    "Vyjayanthi Chari",
    "R. J. Dolbin",
    "T. Ridenour"
  ],
  "comment": "14 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study ad-nilpotent ideals of a parabolic subalgebra of a simple Lie algebra. Any such ideal determines an antichain in a set of positive roots of the simple Lie algebra. We give a necessary and sufficient condition for an antichain to determine an ad-nilpotent ideal of the parabolic. We write down all such antichains for the classical simple Lie algebras and in particular recover the results of D. Peterson. In section 2 of the paper we study the unique ideal in a parabolic which is irreducible as a module for the reductive part and give several equivalent statements that are satisfied by the corresponding subset of roots.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-01T13:50:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B20"
    ],
    "keywords": [
      "parabolic subalgebra",
      "classical simple lie algebras",
      "study ad-nilpotent ideals",
      "ideal determines",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.0245C"
    }
  }
}