{
  "id": "1606.00344",
  "version": "v1",
  "published": "2016-06-01T16:14:48.000Z",
  "updated": "2016-06-01T16:14:48.000Z",
  "title": "Local equivalence of representations of Diff$^+(S^1)$ corresponding to different highest weights",
  "authors": [
    "Mihály Weiner"
  ],
  "comment": "15 pages, no figures",
  "categories": [
    "math-ph",
    "math.MP",
    "math.OA",
    "math.RT"
  ],
  "abstract": "Let $c,h$ and $c,\\tilde{h}$ be two admissible pairs of central charge and highest weight for ${\\rm Diff}^+(S^1)$. It is shown here that the positive energy irreducible projective unitary representations $U_{c,h}$ and $U_{c,\\tilde{h}}$ of the group ${\\rm Diff}^+(S^1)$ are locally equivalent. This means that for any $I\\Subset S^1$ open proper interval, there exists a unitary operator $W_I$ such that $W_I U_{c,h}(\\gamma)W_I^* = U_{c,\\tilde{h}}(\\gamma)$ for all $\\gamma \\in {\\rm Diff}^+(S^1)$ which act identically on $I^c\\equiv S^1\\setminus I$ (i.e. which can \"displace\" or \"move\" points only in $I$). This result extends and completes earlier ones that dealt with only certain regions of the \"$c,h$-plane\", and closes the gap in the full classification of superselection sectors of Virasoro nets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-01T16:14:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81R10"
    ],
    "keywords": [
      "highest weight",
      "local equivalence",
      "energy irreducible projective unitary representations",
      "open proper interval",
      "positive energy irreducible projective unitary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}