{
  "id": "hep-th/0504093",
  "version": "v4",
  "published": "2005-04-11T14:05:05.000Z",
  "updated": "2006-07-05T18:23:24.000Z",
  "title": "Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center",
  "authors": [
    "BL Feigin",
    "AM Gainutdinov",
    "AM Semikhatov",
    "IYu Tipunin"
  ],
  "comment": "LaTeX, amsart++, xy, 51 pages. V3: minor changes, some factors of $i$ sorted out, a reference added. V4: the very final version, very minor changes",
  "journal": "Commun.Math.Phys. 265 (2006) 47-93",
  "doi": "10.1007/s00220-006-1551-6",
  "categories": [
    "hep-th",
    "cond-mat.mes-hall",
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "The SL(2,Z) representation $\\pi$ on the center of the restricted quantum group U_{q}sl(2) at the primitive 2p-th root of unity is shown to be equivalent to the SL(2,Z) representation on the extended characters of the logarithmic (1,p) conformal field theory model. The multiplicative Jordan decomposition of the U_{q}sl(2) ribbon element determines the decomposition of $\\pi$ into a ``pointwise'' product of two commuting SL(2,Z) representations, one of which restricts to the Grothendieck ring; this restriction is equivalent to the SL(2,Z) representation on the (1,p)-characters, related to the fusion algebra via a nonsemisimple Verlinde formula. The Grothendieck ring of U_{q}sl(2) at the primitive 2p-th root of unity is shown to coincide with the fusion algebra of the (1,p) logarithmic conformal field theory model. As a by-product, we derive q-binomial identities implied by the fusion algebra realized in the center of~U_{q}sl(2).",
  "revisions": [
    {
      "version": "v4",
      "updated": "2006-07-05T18:23:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "logarithmic conformal field theory",
      "quantum group center",
      "modular group representations",
      "conformal field theory model",
      "fusion algebra"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "year": 2006,
      "month": "Jul",
      "volume": 265,
      "number": 1,
      "pages": 47
    },
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 680311,
      "adsabs": "2006CMaPh.265...47F"
    }
  }
}