On ${U}(\mathfrak{h})$-free modules over $\mathfrak{sl}(m|n)$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917049098305536 |
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| author | Dimitrov, Ivan Nguyen, Khoa |
| author_facet | Dimitrov, Ivan Nguyen, Khoa |
| contents | We study two categories of ${U}(\mathfrak h)$-free $\mathfrak{sl}(m|n)$-modules of total rank 2: $\mathcal{M}_{\mathfrak{sl}(m|n)}(2)$, whose objects are free of rank 2 over ${U}(\mathfrak h)$ which are not necessarily $\mathbb Z_2$-graded, and $\mathcal{M}_{\mathfrak{sl}(m|n)}(1|1)$, whose objects are supermodules with even and odd parts each isomorphic to ${U}(\mathfrak h)$. For $\mathfrak{sl}(m|1)$ we give a complete classification in both categories, and we prove that for $m,n\geq 2$ both categories are empty. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24921 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On ${U}(\mathfrak{h})$-free modules over $\mathfrak{sl}(m|n)$ Dimitrov, Ivan Nguyen, Khoa Representation Theory 17A70, 17B10 We study two categories of ${U}(\mathfrak h)$-free $\mathfrak{sl}(m|n)$-modules of total rank 2: $\mathcal{M}_{\mathfrak{sl}(m|n)}(2)$, whose objects are free of rank 2 over ${U}(\mathfrak h)$ which are not necessarily $\mathbb Z_2$-graded, and $\mathcal{M}_{\mathfrak{sl}(m|n)}(1|1)$, whose objects are supermodules with even and odd parts each isomorphic to ${U}(\mathfrak h)$. For $\mathfrak{sl}(m|1)$ we give a complete classification in both categories, and we prove that for $m,n\geq 2$ both categories are empty. |
| title | On ${U}(\mathfrak{h})$-free modules over $\mathfrak{sl}(m|n)$ |
| topic | Representation Theory 17A70, 17B10 |
| url | https://arxiv.org/abs/2510.24921 |