2006/02/06 by Yuly Billig, Billig, Yuly
Mathematics · Physics and Astronomy · #17B10 #17B65 #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.RT #msc:17B10 #msc:17B65 #msc:17B69
paper · pdf · doi:10.48550/arxiv.math/0602112
Missing factor of 2 inserted in the Sugawara formula (3.2). Proofs are not affected
openalex publication_date 2006/02/06 · arxiv created 2009/10/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the representation theory for the toroidal extended affine Lie algebras is controlled by a vertex operator algebra which is a tensor product of four VOAs: a sub-VOA of the hyperbolic lattice VOA, two affine VOAs and a Virasoro VOA. A tensor product of irreducible modules for these VOAs admits the structure of an irreducible module for the toroidal extended affine Lie algebra. We also show that for N=12, the sub-VOA of the hyperbolic lattice VOA becomes an exceptional irreducible module for the extended affine Lie algebra of rank 0.