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

2011/02/28 by P. V. Bushlanov, Pavel V. Bushlanov, Azat M. Gainutdinov +2 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Equivalence (formal languages) #Fusion #Linguistics #Logarithm #Mathematical analysis #Mathematics #Philosophy #Pure mathematics #hep-th #math-ph #math.MP #math.QA

paper · pdf · doi:10.1016/j.nuclphysb.2012.04.018

published as Nucl. Phys. B 862 (2012) 232-269 · 40pp. V2: a new introduction, corrected typos, some explanatory comments added, references added

arxiv created 2011/11/08 · openalex publication_date 2012/04/21 · arxiv updated 2015/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

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Cited by

• Lattice W-algebras and logarithmic CFTs