{
  "id": "math/0603685",
  "version": "v2",
  "published": "2006-03-29T15:38:19.000Z",
  "updated": "2009-06-03T16:00:15.000Z",
  "title": "Orbital Varieties and Unipotent Representations",
  "authors": [
    "Thomas Pietraho"
  ],
  "comment": "35 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Using the notion of a Lagrangian covering, W. Graham and D. Vogan proposed a method of constructing representations from the coadjoint orbits for a complex semisimple Lie group $G$. When the coadjoint orbit $\\calO$ is nilpotent, a representation of $G$ is attached to each orbital variety of $\\calO$ in this way. In the setting of classical groups, we show that whenever it is possible to carry out the Graham-Vogan construction for an orbital variety of a spherical $\\mathcal{O}$, its infinitesimal character lies in a set of characters attached to $\\mathcal{O}$ by W. M. McGovern. Furthermore, we show that it is possible to carry out the Graham-Vogan construction for a sufficient number of orbital varieties to account for all the infinitesimal characters in this set.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-06-03T16:00:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46"
    ],
    "keywords": [
      "orbital variety",
      "unipotent representations",
      "coadjoint orbit",
      "graham-vogan construction",
      "complex semisimple lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3685P"
    }
  }
}