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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.06898 |
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| _version_ | 1866912411842248704 |
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| author | Chen, Haibo Su, Yucai Xiao, Yukun |
| author_facet | Chen, Haibo Su, Yucai Xiao, Yukun |
| contents | 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 $t\in \frac{1}{2}+\Z_+$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06898 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Restricted representations of the twisted $N=2$ superconformal algebra Chen, Haibo Su, Yucai Xiao, Yukun Representation Theory 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 $t\in \frac{1}{2}+\Z_+$. |
| title | Restricted representations of the twisted $N=2$ superconformal algebra |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2303.06898 |