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

Abstract

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 $\mathcal{O}$ as modules for the associated affine Lie algebra. We classify irreducible objects in that category and prove semisimplicity of that category.

arXiv comment21 pages, LaTeX