engleski

On the representation theory of $L_{;;;-5/2};;;(sl(4))$

We consider simple affine vertex algebra $L_{; ; ; -5/2}; ; ; (sl(4))$. Using an explicit formula for a singular vector, Zhu’s theory and the conformal embeddings, we obtain classification of irreducible $L_{; ; ; -5/2}; ; ; (sl(4))$-modules in the category O. We also determine fusion rules for irreducible $L_{; ; ; -5/2}; ; ; (sl(4))$-modules in the category of ordinary modules.

representation theory ; vertex algebras ; vertex operator algebras ; fusion rules ; conformal embeddings

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