Vertex operator algebras associated to modified regular representations of the Virasoro algebra

2010/12/25 by Igor Frenkel, Frenkel, Igor, Minxian Zhu +1
Mathematics · Physics and Astronomy · #17B68 #17B69 #33C05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:17B68 #msc:17B69 #msc:33C05

paper · pdf · doi:10.48550/arxiv.1012.5443

29 pages

arxiv created 2010/12/25 · openalex publication_date 2010/12/25 · arxiv updated 2010/12/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We give an abstract construction, based on the Belavin-Polyakov-Zamolodchikov equations, of a family of vertex operator algebras of rank 26 associated to the modified regular representations of the Virasoro algebra. The vertex operators are obtained from the tensor products of intertwining operators for a pair of Virasoro algebras. We explicitly determine the structure coefficients that yield the axioms of VOAs. In the process of our construction, we obtain new hypergeometric identities.

Citations

• Infinite conformal symmetry in two-dimensional quantum field theory

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