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

Abstract

Let L(− 1 (l+1),0) be the simple vertex operator algebra associated to an affine Lie algebra of typeA (1) with the lowest admissible halfinteger level − 1 (l + 1), for even l. We study the category of weak modules for that vertex operator algebra which are in category O as modules for the associated affine Lie algebra. We classify irreducible objects in that category and prove semisimplicity of that category.