engleski

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

Let $L(n-l+\frac{; ; 1}; ; {; ; 2}; ; , 0)$ be the vertex operator algebra associated to an affine Lie algebra of type $B_{; ; l}; ; ^{; ; (1)}; ; $ at level $n-l+\frac{; ; 1}; ; {; ; 2}; ; $, for a positive integer $n$. We classify irreducible $L(n-l+\frac{; ; 1}; ; {; ; 2}; ; , 0)$-modules and show that every $L(n-l+\frac{; ; 1}; ; {; ; 2}; ; , 0)$-module is completely reducible. In the special case $n=1$, we study a category of weak $L(-l+\frac{; ; 3}; ; {; ; 2}; ; , 0)$-modules which are in the category $\mathcal{; ; O}; ; $ as modules for the associated affine Lie algebra. We classify irreducible objects in that category and prove semisimplicity of that category.

vertex operator algebras; affine Kac-Moody algebras; admissible modules

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