A category of modules for the full toroidal Lie algebra

Details A category of modules for the full toroidal Lie algebra A category of modules for the full toroidal Lie algebra

2005-09-16

arxiv.org/abs/math/0509368v2

Mathematics

Representation Theory

Missing factor of 2 inserted in the Sugawara formulas (3.20), (3.21) and Theorem 5.4. Proofs are not affected

Scientific paper

We introduce a category B of bounded modules for the toroidal Lie algebras and study irreducible modules in B. We show that one of the irreducible modules in this category, L(T_0), admits a structure of a vertex operator algebra. We prove that L(T_0) factors into a tensor product of a sub-VOA of a hyperbolic lattice VOA and a simple VOA associated with a twisted Virasoro-affine Lie algebra. Every irreducible module in category B is a VOA module for a slightly larger VOA V(T_0). Knowing the structure of V(T_0), we are able to give explicit realizations for all irreducible modules in category B and determine their characters.

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