Fusion rules for V_{L_2}^{S_4}
This paper determines the fusion rules for the fixed-point vertex operator algebra $V_{L_2}^{S_4}$, where $L_2$ denotes the rank-one even lattice satisfying $(\alpha,\alpha)=2$. The main idea is to identify certain irreducible $V_{\mathbb Z\zeta}^{+}$-modules as direct sums of irreducible $V_{L_2}^{S_4}$-modules. These identifications allow us to compute the relevant entries of the $S$-matrix for $V_{L_2}^{S_4}$. Applying the Verlinde formula, we then obtain the complete fusion rules for $V_{L_2}^{S_4}$.
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