Representations of toroidal extended affine Lie algebras

Yuly Billig

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Representations of toroidal extended affine Lie algebras

Yuly Billig

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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.

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Yuly Billig. 2009-10-13. Representations of toroidal extended affine Lie algebras. https://arxiv.org/abs/math/0602112

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