Non-weight modules over gap-$p$ Virasoro algebras
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912385476853760 |
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| author | Xu, Chengkang Chen, Fulin Tan, Shaobin |
| author_facet | Xu, Chengkang Chen, Fulin Tan, Shaobin |
| contents | In this paper, we study non-weight modules over gap-$p$ Virasoro algebras, including Whittaker modules, $\mathcal{U}(\mathbb{C} L_0)$-free modules and their tensor products. We establish necessary and sufficient conditions for universal Whittaker modules to be irreducible and study the structure of irreducible Whittaker modules. The $\mathcal{U}(\mathbb{C} L_0)$-free modules of rank 1 are classified and the irreducibility of such modules are determined. Moreover, the irreducibility of tensor products of $\mathcal{U}(\mathbb{C} L_0)$-free modules of rank 1 and irreducible restricted modules is also determined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15273 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-weight modules over gap-$p$ Virasoro algebras Xu, Chengkang Chen, Fulin Tan, Shaobin Representation Theory 17B10, 17B65, 17B66, 17B68, 17B69 In this paper, we study non-weight modules over gap-$p$ Virasoro algebras, including Whittaker modules, $\mathcal{U}(\mathbb{C} L_0)$-free modules and their tensor products. We establish necessary and sufficient conditions for universal Whittaker modules to be irreducible and study the structure of irreducible Whittaker modules. The $\mathcal{U}(\mathbb{C} L_0)$-free modules of rank 1 are classified and the irreducibility of such modules are determined. Moreover, the irreducibility of tensor products of $\mathcal{U}(\mathbb{C} L_0)$-free modules of rank 1 and irreducible restricted modules is also determined. |
| title | Non-weight modules over gap-$p$ Virasoro algebras |
| topic | Representation Theory 17B10, 17B65, 17B66, 17B68, 17B69 |
| url | https://arxiv.org/abs/2505.15273 |