Representations of toroidal extended affine Lie algebras
Representation Theory
2009-10-13 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0602112,
title = {Representations of toroidal extended affine Lie algebras},
author = {Yuly Billig},
journal= {arXiv preprint arXiv:math/0602112},
year = {2009}
}
Comments
Missing factor of 2 inserted in the Sugawara formula (3.2). Proofs are not affected