dc.contributor.author Ramgoolam, S dc.date.accessioned 2016-04-01T15:10:58Z dc.date.issued 1993 dc.date.submitted 2016-03-10T16:59:17.638Z dc.identifier.uri http://qmro.qmul.ac.uk/xmlui/handle/123456789/11617 dc.description 30 pages (minor typos corrected, refs added) dc.description.abstract We show that the Hopf link invariants for an appropriate set of finite dimensional representations of $U_q SL(2)$ are identical, up to overall normalisation, to the modular S matrix of Kac and Wakimoto for rational $k$ $\widehat {sl(2)}$ representations. We use this observation to construct new modular Hopf algebras, for any root of unity $q=e^{-i\pi m/r}$, obtained by taking appropriate quotients of $U_q SL(2)$, that give rise to 3-manifold invariants according to the approach of Reshetikin and Turaev. The phase factor correcting for the `framing anomaly' in these invariants is equal to $e^{- {{i \pi} \over 4} ({ {3k} \over {k+2}})}$, an analytic continuation of the anomaly at integer $k$. As expected, the Verlinde formula gives fusion rule multiplicities in agreement with the modular Hopf algebras. This leads to a proposal, for $(k+2)=r/m$ rational with an odd denominator, for a set of $\widehat {sl(2)}$ representations obtained by dropping some of the highest weight representations in the Kac-Wakimoto set and replacing them with lowest weight representations. For this set of representations the Verlinde formula gives non-negative integer fusion rule multiplicities. We discuss the consistency of the truncation to highest and lowest weight representations in conformal field theory. dc.subject hep-th dc.subject hep-th dc.subject math.QA dc.title New Modular Hopf Algebras related to rational $k$ $\widehat {sl(2)}$ dc.type Journal Article pubs.author-url http://arxiv.org/abs/hep-th/9301121v2 pubs.organisational-group /Queen Mary University of London pubs.organisational-group /Queen Mary University of London/Faculty of Science & Engineering pubs.organisational-group /Queen Mary University of London/Faculty of Science & Engineering/Physics and Astronomy
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