{
  "id": "0810.4600",
  "version": "v1",
  "published": "2008-10-25T13:41:47.000Z",
  "updated": "2008-10-25T13:41:47.000Z",
  "title": "Ad-nilpotent Ideals and Equivalence Relations",
  "authors": [
    "Chuying Fang"
  ],
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "In this paper we study ad-nilpotent ideals of a complex simple Lie algebra $\\ccg$ and their connections with affine Weyl groups and nilpotent orbits. We define a left equivalence relation for ad-nilpotent ideals based on their normalizer and generators, and prove that the equivalence relation is compatible with the left cell structure of affine Weyl group of $\\ccg$ and Lusztig's star operator for type $\\tilde A_{n-1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-25T13:41:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine weyl group",
      "complex simple lie algebra",
      "lusztigs star operator",
      "left equivalence relation",
      "left cell structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.4600F"
    }
  }
}