Kazhdan-Lusztig equivalence and fusion of Kac modules in Virasoro logarithmic models

Details Kazhdan-Lusztig equivalence and fusion of Kac modules in Virasoro logarithmic models Kazhdan-Lusztig equivalence and fusion of Kac modules in Virasoro logarithmic models

2011-02-01

arxiv.org/abs/1102.0271v2

Physics

High Energy Physics

High Energy Physics - Theory

40pp. V2: a new introduction, corrected typos, some explanatory comments added, references added

Scientific paper

The subject of our study is the Kazhdan-Lusztig (KL) equivalence in the context of a one-parameter family of logarithmic CFTs based on Virasoro symmetry with the (1,p) central charge. All finite-dimensional indecomposable modules of the KL-dual quantum group - the "full" Lusztig quantum sl(2) at the root of unity - are explicitly described. These are exhausted by projective modules and four series of modules that have a functorial correspondence with any quotient or a submodule of Feigin-Fuchs modules over the Virasoro algebra. Our main result includes calculation of tensor products of any pair of the indecomposable modules. Based on the Kazhdan-Lusztig equivalence between quantum groups and vertex-operator algebras, fusion rules of Kac modules over the Virasoro algebra in the (1,p) LCFT models are conjectured.

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