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

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 $c_{p,p^{\prime }}=3\left(1-\frac{2p^{\prime }}{p}\right)$ 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 $c_{3,2}=-1$.

arXiv comment18 pages

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Cited by in corpus (2)

• Duality of subregular W-algebras and principal W-superalgebras
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