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

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

2005-12-06

arxiv.org/abs/math/0512129v2

J. Algebra 307 (2007), 215-248

Mathematics

Quantum Algebra

40 pages, LaTeX; minor changes

Scientific paper

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 $\cal{O}$ 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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