On non-weight representations of the $N=2$ superconformal algebras

Hengyun Yang; Yufeng Yao; Limeng Xia

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arXiv · 1910.08961

On non-weight representations of the $N=2$ superconformal algebras

Hengyun Yang·Yufeng Yao·Limeng Xia

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Abstract

In this paper, we construct a family of non-weight modules over the untwisted $N=2$ superconformal algebras. Those modules when regarded as modules over the Cartan subalgebra (modulo the center) are free of rank $2$. We give a classification of isomorphism classes of such modules. Moreover, all submodules of such modules are precisely determined. In particular, those modules are not simple. The corresponding simple quotient modules are classified. Furthermore, these simple modules when restricted as modules over $N=1$ superconformal algebras coincide with those modules constructed in [H. Yang, Y. Yao, L. Xia, A family of non-weight modules over the super-Virasoro algebras, J. Algebra 547 (2020), 538-555].

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BibTeX RIS

Hengyun Yang, Yufeng Yao, Limeng Xia. 2020-07-08. On non-weight representations of the $N=2$ superconformal algebras. https://arxiv.org/abs/1910.08961

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