Kazhdan--Lusztig-dual quantum group for logarithmic extensions of Virasoro minimal models

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dc.creatorFeigin, BL
dc.creatorGainutdinov, AM
dc.creatorSemikhatov, AM
dc.creatorTipunin, IYu
dc.date2006-06-20
dc.date2007-01-16
dc.date.accessioned2026-07-07T11:07:21Z
dc.date.available2026-07-07T11:07:21Z
dc.descriptionWe derive and study a quantum group g(p,q) that is Kazhdan--Lusztig-dual to the W-algebra W(p,q) of the logarithmic (p,q) conformal field theory model. The algebra W(p,q) is generated by two currents $W^+(z)$ and $W^-(z)$ of dimension (2p-1)(2q-1), and the energy--momentum tensor T(z). The two currents generate a vertex-operator ideal $R$ with the property that the quotient W(p,q)/R is the vertex-operator algebra of the (p,q) Virasoro minimal model. The number (2 p q) of irreducible g(p,q)-representations is the same as the number of irreducible W(p,q)-representations on which $R$ acts nontrivially. We find the center of g(p,q) and show that the modular group representation on it is equivalent to the modular group representation on the W(p,q) characters and ``pseudocharacters.'' The factorization of the g(p,q) ribbon element leads to a factorization of the modular group representation on the center. We also find the g(p,q) Grothendieck ring, which is presumably the ``logarithmic'' fusion of the (p,q) model.
dc.description52pp., AMSLaTeX++. half a dozen minor inaccuracies (cross-refs etc) corrected
dc.identifierhttps://arxiv.org/abs/math/0606506
dc.identifierhttp://arxiv.org/abs/math/0606506
dc.identifierJ.Math.Phys.48:032303,2007
dc.identifierdoi:10.1063/1.2423226
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/189816
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectRepresentation Theory
dc.titleKazhdan--Lusztig-dual quantum group for logarithmic extensions of Virasoro minimal models
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