Representations of toroidal extended affine Lie algebras

Details Representations of toroidal extended affine Lie algebras Representations of toroidal extended affine Lie algebras

2006-02-06

arxiv.org/abs/math/0602112v2

Mathematics

Representation Theory

Missing factor of 2 inserted in the Sugawara formula (3.2). Proofs are not affected

Scientific paper

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.

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