Vertex operator algebras associated to type B affine Lie algebras on admissible half-integer levels

Let L(n - l + 1/2, 0) be the vertex operator algebra associated to an affine Lie algebra of type BM at level 21 1 n - I + 1/2 for a positive integer n. We classify irreducible L(n - l + 1/2, 0)-modules and show that every L (n - 1 + 1/2, 0)-module is completely reducible. In the special case n 1, we study a category of weak 2, 0)-modules which are in the category 0 as modules for the associated affine Lie algebra. We L(-l + 3/2, 0) classify irreducible objects in that category and prove semisimplicity of that category. (C) 2006 Elsevier Inc. All rights reserved.