Generalized permutation matrices and non-weight modules over $\mathfrak{sl}(m|1)$
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914116240670720 |
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| author | Dimitrov, Ivan Nguyen, Khoa Paquette, Charles Wehlau, David |
| author_facet | Dimitrov, Ivan Nguyen, Khoa Paquette, Charles Wehlau, David |
| contents | We study the category $\mathcal{M}_{\mathfrak{sl}(m|1)}(k|k)$ of $\mathcal U(\mathfrak h)\text{-free}$ $\mathcal U(\mathfrak{sl}(m|1))$-modules of rank $k$ in each parity (rank $(k|k)$), where $k\in\mathbb{Z}_{\geq1}$. We construct an explicit family of such modules, provide an isomorphism theorem, and establish an indecomposability criterion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22877 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized permutation matrices and non-weight modules over $\mathfrak{sl}(m|1)$ Dimitrov, Ivan Nguyen, Khoa Paquette, Charles Wehlau, David Representation Theory 17A70, 17B10 We study the category $\mathcal{M}_{\mathfrak{sl}(m|1)}(k|k)$ of $\mathcal U(\mathfrak h)\text{-free}$ $\mathcal U(\mathfrak{sl}(m|1))$-modules of rank $k$ in each parity (rank $(k|k)$), where $k\in\mathbb{Z}_{\geq1}$. We construct an explicit family of such modules, provide an isomorphism theorem, and establish an indecomposability criterion. |
| title | Generalized permutation matrices and non-weight modules over $\mathfrak{sl}(m|1)$ |
| topic | Representation Theory 17A70, 17B10 |
| url | https://arxiv.org/abs/2510.22877 |