Serre functors for Lie superalgebras and tensoring with $S^{\mathrm{top}}(\mathfrak{g}_{\overline{1}})$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915275316658176 |
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| author | Chen, Chih-Whi Mazorchuk, Volodymyr |
| author_facet | Chen, Chih-Whi Mazorchuk, Volodymyr |
| contents | We show that the action of the Serre functor on the subcategory of projective-injective modules in a parabolic BGG category $\mathcal O$ of a quasi-reductive finite dimensional Lie superalgebra is given by tensoring with the top component of the symmetric power of the odd part of our superalgebra. As an application, we determine, for all strange Lie suepralgebras, when the subcategory of projective injective modules in the parabolic category $\mathcal O$ is symmetric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03197 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Serre functors for Lie superalgebras and tensoring with $S^{\mathrm{top}}(\mathfrak{g}_{\overline{1}})$ Chen, Chih-Whi Mazorchuk, Volodymyr Representation Theory 17B10, 17B55 We show that the action of the Serre functor on the subcategory of projective-injective modules in a parabolic BGG category $\mathcal O$ of a quasi-reductive finite dimensional Lie superalgebra is given by tensoring with the top component of the symmetric power of the odd part of our superalgebra. As an application, we determine, for all strange Lie suepralgebras, when the subcategory of projective injective modules in the parabolic category $\mathcal O$ is symmetric. |
| title | Serre functors for Lie superalgebras and tensoring with $S^{\mathrm{top}}(\mathfrak{g}_{\overline{1}})$ |
| topic | Representation Theory 17B10, 17B55 |
| url | https://arxiv.org/abs/2505.03197 |