{
  "id": "2003.00988",
  "version": "v1",
  "published": "2020-03-02T16:13:16.000Z",
  "updated": "2020-03-02T16:13:16.000Z",
  "title": "Connections between the representation theory of $sl_2 ( \\mathbb{C} )$ and the Virasoro algebra",
  "authors": [
    "Matthew Ondrus",
    "Emilie Wiesner"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "The Lie algebra $sl_2 ( \\mathbb{C} )$ may be regarded in a natural way as a subalgebra of the infinite-dimensional Virasoro Lie algebra, and this suggests there may be connections between the representation theory of the two algebras. In this paper, we explore the restriction to $sl_2 ( \\mathbb{C} )$ of certain induced modules for the Virasoro algebra. Specifically, we consider Virasoro modules induced from so-called polynomial subalgebras, and we show that the restriction of these modules results in twisted versions of familiar modules such as Verma modules and Whittaker modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-02T16:13:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B68",
      "17B10",
      "17B65"
    ],
    "keywords": [
      "representation theory",
      "virasoro algebra",
      "connections",
      "infinite-dimensional virasoro lie algebra",
      "whittaker modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}