{
  "id": "math/0402140",
  "version": "v3",
  "published": "2004-02-09T13:06:52.000Z",
  "updated": "2004-05-20T12:32:05.000Z",
  "title": "Normalizers of ad-nilpotent ideals",
  "authors": [
    "Dmitri I. Panyushev"
  ],
  "comment": "26 pages; New section 4 is added; References added",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "Let $\\be$ be a Borel subalgebra of a complex simple Lie algebra $\\g$. An ideal of $\\be$ is called ad-nilpotent, if it is contained in $[\\be,\\be]$. We give several descriptions of the normalizer of an ad-nilpotent ideal: using the weight of an ideal, or the affine Weyl group, or a relationship with dominant regions of the Shi arrangement. We also give a description of those ideals whose normalizer is equal to $\\be$. For sl(n) and sp(2n), explicit enumerative results are obtained, which demonstrate a connection with some famous integer sequences.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-05-20T12:32:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B20"
    ],
    "keywords": [
      "ad-nilpotent ideal",
      "normalizer",
      "complex simple lie algebra",
      "affine weyl group",
      "dominant regions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2140P"
    }
  }
}