engleski

Vertex operator algebra analogue of embedding of $B_4$ into $F_4$

Let $L_{; ; B}; ; (-\frac{; ; 5}; ; {; ; 2}; ; , 0)$ (resp. $L_{; ; F}; ; (-\frac{; ; 5}; ; {; ; 2}; ; , 0)$) be the simple vertex operator algebra associated to affine Lie algebra of type $B_{; ; 4}; ; ^{; ; (1)}; ; $ (resp. $F_{; ; 4}; ; ^{; ; (1)}; ; $) with the lowest admissible half-integer level $-\frac{; ; 5}; ; {; ; 2}; ; $. We show that $L_{; ; B}; ; (-\frac{; ; 5}; ; {; ; 2}; ; , 0)$ is a vertex subalgebra of $L_{; ; F}; ; (-\frac{; ; 5}; ; {; ; 2}; ; , 0)$ with the same conformal vector, and that $L_{; ; F}; ; (-\frac{; ; 5}; ; {; ; 2}; ; , 0)$ is isomorphic to the extension of $L_{; ; B}; ; (-\frac{; ; 5}; ; {; ; 2}; ; , 0)$ by its only irreducible module other than itself. We also study the representation theory of $L_{; ; F}; ; (-\frac{; ; 5}; ; {; ; 2}; ; , 0)$, and determine the decompositions of irreducible weak $L_{; ; F}; ; (-\frac{; ; 5}; ; {; ; 2}; ; , 0)$-modules from the category $\mathcal{; ; O}; ; $ into direct sums of irreducible weak $L_{; ; B}; ; (-\frac{; ; 5}; ; {; ; 2}; ; , 0)$-modules.

vertex operator algebra; affine Kac-Moody algebra; admissible module; extension of vertex operator algebra

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