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arXiv · 1810.13147

On resolution of highest weight modules over the $\mathcal{N}=2$ superconformal algebra

Shinji Koshida·Ryo Sato
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Abstract

In this paper we construct Bernstein--Gelfand--Gelfand type resolution of simple highest weight modules over the simple $\mathcal{N}=2$ vertex operator superalgebra of central charge $c_{p,p'}=3\left(1-\frac{2p'}{p}\right)$ by means of the Kazama--Suzuki coset construction. As an application, we compute the twisted Zhu algebras of the simple $\mathcal{N}=2$ vertex operator superalgebra. We also compute the Frenkel--Zhu bimodule structure associated with a certain simple highest weight module of central charge $c_{3,2}=-1$.

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Shinji Koshida, Ryo Sato. 2018-10-31. On resolution of highest weight modules over the $\mathcal{N}=2$ superconformal algebra. https://arxiv.org/abs/1810.13147

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