Simple $\mathfrak{sl}_2$-modules that are torsion free $U(\mathfrak{h})$-modules of rank $1$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908866177925120 |
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| author | Grantcharov, Dimitar Krizka, Libor Mazorchuk, Volodymyr |
| author_facet | Grantcharov, Dimitar Krizka, Libor Mazorchuk, Volodymyr |
| contents | We provide an explicit classification of all simple $\mathfrak{sl}_2$-modules that are torsion free of rank $1$ over the Cartan subalgebra. We also establish a similar result for the first Weyl algebra and for the Lie superalgebra $\mathfrak{osp}(1|2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04303 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simple $\mathfrak{sl}_2$-modules that are torsion free $U(\mathfrak{h})$-modules of rank $1$ Grantcharov, Dimitar Krizka, Libor Mazorchuk, Volodymyr Representation Theory We provide an explicit classification of all simple $\mathfrak{sl}_2$-modules that are torsion free of rank $1$ over the Cartan subalgebra. We also establish a similar result for the first Weyl algebra and for the Lie superalgebra $\mathfrak{osp}(1|2)$. |
| title | Simple $\mathfrak{sl}_2$-modules that are torsion free $U(\mathfrak{h})$-modules of rank $1$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2603.04303 |