Quantum SL(2) and logarithmic vertex operator algebras at (p,1)-central charge

Abstract

We provide a ribbon tensor equivalence between the representation category of small quantum SL(2), at parameter q=exp($\pi$ i/p), and the representation category of the triplet vertex operator algebra at integral parameter p>1. We provide similar quantum group equivalences for representation categories associated to the Virasoro, and singlet vertex operator algebras at central charge c=1-6(p-1)^2/p. These results resolve a number of fundamental conjectures coming from studies of logarithmic CFTs in type A_1.

arXiv comment50 pages

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Cited by in corpus (7)

• Ribbon tensor structure on the full representation categories of the singlet vertex algebras
• Characterizing braided tensor categories associated to logarithmic vertex operator algebras
• Fusion and (non)-rigidity of Virasoro Kac modules in logarithmic minimal models at $(p,q)$-central charge
• On rationality for $C_2$-cofinite vertex operator algebras
• Support theory for Drinfeld doubles of some infinitesimal group schemes
• Fibre functors and reconstruction of Hopf algebras
• Algebras of Non-Local Screenings and Diagonal Nichols Algebras