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

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arxiv 2104.12821 v1 pith:X7F5KRR2 submitted 2021-04-26 math.QA math-phmath.MPmath.RT

Terry Gannon , Cris Negron This is my paper · ORCID
classification math.QAmath-phmath.MPmath.RT
keywords operatorquantumrepresentationvertexalgebrascategorycentralcharge
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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.

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  1. Tensor structure on the module category of the triplet superalgebra $\mathcal{{SW}}(m)$

    math.QA 2024-12 conditional novelty 7.0 of 10

    For each m, the tensor supercategory on SW(m)-mod is rigid, all simple and projective modules are self-dual, and the fusion ring is generated by one simple module X2.

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