Vertex operator algebras associated to type B affine Lie algebras on admissible half-integer levels
arXiv:math/0512129
Abstract
Let L(n-l+1/2,0) be the vertex operator algebra associated to an affine Lie algebra of type B_l^(1) at level n-l+1/2, for a positive integer n. We classify irreducible L(n-l+1/2,0)-modules and show that every L(n-l+1/2,0)-module is completely reducible. In the special case n=1, we study a category of weak L(-l+3/2,0)-modules which are in the category as modules for the associated affine Lie algebra. We classify irreducible objects in that category and prove semisimplicity of that category.
arXiv comment40 pages, LaTeX; minor changes