Vertex operator algebras associated to certain admissible modules for affine Lie algebras of type A

Details Vertex operator algebras associated to certain admissible modules for affine Lie algebras of type A Vertex operator algebras associated to certain admissible modules for affine Lie algebras of type A

2007-07-27

arxiv.org/abs/0707.4129v1

Glas. Mat. Ser. III 43 (63) 2008, 41-57

Mathematics

Quantum Algebra

21 pages, LaTeX

Scientific paper

Let $L(-{1/2}(l+1),0)$ be the simple vertex operator algebra associated to an affine Lie algebra of type $A_{l}^{(1)}$ with the lowest admissible half-integer level $-{1/2}(l+1)$, for even l. We study the category of weak modules for that vertex operator algebra which are in category $\cal{O}$ as modules for the associated affine Lie algebra. We classify irreducible objects in that category and prove semisimplicity of that category.

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