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International Mathematics Research Notices (2006) Vol. 2006 : article ID 68395, 46 pages, doi:10.1155/IMRN/2006/68395
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Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

A category of modules for the full toroidal Lie algebra

Yuly Billig

School of Mathematics and Statistics, Carleton University 1125 Colonel By Drive, Ottawa, ON, Canada K1S 5B6 E-mail address: billig{at}math.carleton.ca

We define a category of bounded modules for the full toroidal Lie algebra, classify irreducible modules in this category, and give their explicit vertex operator realizations. Using the technique of vertex algebras, we prove that for a generic level such modules decompose into a tensor product of five factors, which are simple modules for a sub-VOA of a lattice VOA, two affine Lie algebras, a Heisenberg algebra, and a Virasoro algebra.

Dedicated to Robert Moody


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