Modified regular representations of affine and Virasoro algebras, VOA structure and semi-infinite cohomology

2004/09/07 by Igor Frenkel, Igor B. Frenkel, Frenkel, Igor B. +2
Mathematics · #17B67 #17B68 #17B69 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:17B67 #msc:17B68 #msc:17B69

paper · pdf · doi:10.48550/arxiv.math/0409117

39 pages

arxiv created 2004/09/07 · openalex publication_date 2004/09/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We identify the algebra of matrix elements of big projective modules in category O with the regular functions on the big Bruhat cell of G. Analogous extensions of the regular representations of the affine Lie and Virasoro algebras yield vertex operator algebras, equipped with two commuting actions with special values of the total central charge. In the generic case, we identify the structure of these VOAs, compute their semi-infinite cohomology. Its superalgebra structure encodes the fusion rules for the associated tensor categories. Full details are provided for the affine sl(2) and Virasoro algebras, and various generalizations and extensions are discussed.

Citations

• Twisted K-theory and loop group representations

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