We derive and study a quantum group that is Kazhdan-Lusztig dual to the -algebra of the logarithmic conformal field theory model. The algebra is generated by two currents and of dimension and the energy-momentum tensor . The two currents generate a vertex-operator ideal with the property that the quotient is the vertex-operator algebra of the Virasoro minimal model. The number of irreducible representations is the same as the number of irreducible representations on which acts nontrivially. We find the center of and show that the modular group representation on it is equivalent to the modular group representation on the characters and “pseudocharacters.” The factorization of the ribbon element leads to a factorization of the modular group representation on the center. We also find the Grothendieck ring, which is presumably the “logarithmic” fusion of the model.
Kazhdan-Lusztig-dual quantum group for logarithimic extensions of Virasoro minimal models
B. L. Feigin, A. M. Gainutdinov, A. M. Semikhatov, I. Yu. Tipunin; Kazhdan-Lusztig-dual quantum group for logarithimic extensions of Virasoro minimal models. J. Math. Phys. 1 March 2007; 48 (3): 032303. https://doi.org/10.1063/1.2423226
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