New Modular Hopf Algebras related to rational
نویسنده
چکیده
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 sl(2) representations. We use this observation to construct new modular Hopf algebras, for any root of unity q = e −iπm/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 − iπ 4 (3k 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 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.
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تاریخ انتشار 1993