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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.12527 |
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| _version_ | 1866913271772086272 |
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| author | Chen, Haibo Dai, Xiansheng Liu, Dong Pei, Yufeng |
| author_facet | Chen, Haibo Dai, Xiansheng Liu, Dong Pei, Yufeng |
| contents | In this paper, we introduce a family of functors denoted $\mathscr{F}_b$ that act on algebraic D-modules and generate modules over N=2 superconformal algebras. We prove these functors preserve irreducibility for all values of $b$, with a few clear exceptions described. We also establish necessary and sufficient conditions to determine when two such functors are naturally isomorphic. Applying $\mathscr{F}_b$ to N=1 super-Virasoro algebras recovers the functors previously introduced in \cite{CDLP}. Our new functors also facilitate the recovery of specific irreducible modules over N=2 superconformal algebras, including intermediate series and $U(\mathfrak{h})$-free modules. Additionally, our constructed functors produce several new irreducible modules for N=2 superconformal algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12527 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Irreducible modules over N=2 superconformal algebras from algebraic D-modules Chen, Haibo Dai, Xiansheng Liu, Dong Pei, Yufeng Representation Theory In this paper, we introduce a family of functors denoted $\mathscr{F}_b$ that act on algebraic D-modules and generate modules over N=2 superconformal algebras. We prove these functors preserve irreducibility for all values of $b$, with a few clear exceptions described. We also establish necessary and sufficient conditions to determine when two such functors are naturally isomorphic. Applying $\mathscr{F}_b$ to N=1 super-Virasoro algebras recovers the functors previously introduced in \cite{CDLP}. Our new functors also facilitate the recovery of specific irreducible modules over N=2 superconformal algebras, including intermediate series and $U(\mathfrak{h})$-free modules. Additionally, our constructed functors produce several new irreducible modules for N=2 superconformal algebras. |
| title | Irreducible modules over N=2 superconformal algebras from algebraic D-modules |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2403.12527 |