Restricted representations of the twisted $N=2$ superconformal algebra

Haibo Chen; Yucai Su; Yukun Xiao

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arXiv · 2303.06898

Restricted representations of the twisted $N=2$ superconformal algebra

Haibo Chen·Yucai Su·Yukun Xiao

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Abstract

In this paper, we construct a large class of new simple modules over the twisted $N=2$ superconformal algebra. These new simple modules are restricted modules based on the simple modules over certain finite-dimensional solvable Lie superalgebras, including various versions of Whittaker modules. We elaborate that they are also the twisted modules for the universal $N=2$ superconformal vertex algebra. On the other hand, we give an explicit characterization of the simple restricted modules over the twisted $N=2$ superconformal algebra $\mathcal{T}$ under the condition that $T_t$ in $\mathcal{T}$ acts injectively for some $t\in \frac{1}{2}+\Z_+$.

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BibTeX RIS

Haibo Chen, Yucai Su, Yukun Xiao. 2023-03-13. Restricted representations of the twisted $N=2$ superconformal algebra. https://arxiv.org/abs/2303.06898

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