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

2021/04/26 by Terry Gannon, Gannon, Terry, Cris Negron +1 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2104.12821

openalex publication_date 2021/04/26 · openalex created_date 2021/05/10 · openalex updated_date 2026/07/28

Abstract

We provide a ribbon tensor equivalence between the representation category of small quantum SL(2), at parameter q=exp(π 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 A₁.

Citations

• Logarithmic CFTs connected with simple Lie algebras
• C₂-cofinite W-algebras and their logarithmic representations

Cited by

• Nichols algebras, tensor categories and Kazhdan-Lusztig correspondences
• A tensor category construction of the W_p,q triplet vertex operator algebra and applications
• The Construction of Correlators in Finite Rigid Logarithmic Conformal Field Theory
• Characterizing braided tensor categories associated to logarithmic vertex operator algebras

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