{
  "id": "2101.08774",
  "version": "v1",
  "published": "2021-01-21T18:55:19.000Z",
  "updated": "2021-01-21T18:55:19.000Z",
  "title": "Approximation of nilpotent orbits for simple Lie groups",
  "authors": [
    "Lucas Fresse",
    "Salah Mehdi"
  ],
  "comment": "31 pages, 4 figures",
  "categories": [
    "math.RT",
    "math.GT"
  ],
  "abstract": "We propose a systematic and topological study of limits of continuous families of adjoint orbits for non-compact simple Lie groups. This limit is always a finite union of nilpotent orbits. We describe explicitly these nilpotent orbits in terms of Richardson orbits in the case of hyperbolic semisimple elements. We also show that one can approximate minimal nilpotent orbits or even nilpotent orbits by elliptic semisimple orbits. The special cases of $\\mathrm{SL}_n(\\mathbb{R})$ and $\\mathrm{SU}(p,q)$ are computed in detail.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-21T18:55:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B08",
      "22E15"
    ],
    "keywords": [
      "approximation",
      "non-compact simple lie groups",
      "approximate minimal nilpotent orbits",
      "elliptic semisimple orbits",
      "hyperbolic semisimple elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}