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arXiv · 2308.15954

Fusion rules for the triplet $W$-algebra $\mathcal{W}_{p_+,p_-}$

Hiromu Nakano
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Abstract

We study the structure of fusion rules for the triplet $W$-algebra $\mathcal{W}_{p_+,p_-}$. By using the vertex tensor category theory developed by Huang, Lepowsky and Zhang, we rederive certain non-semisimple fusion rules given by Gaberdiel-Runkel-Wood and Rasmussen. We further show that certain rank two and three indecomposable modules are self-dual.

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Hiromu Nakano. 2023-08-30. Fusion rules for the triplet $W$-algebra $\mathcal{W}_{p_+,p_-}$. https://arxiv.org/abs/2308.15954

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