Exponential modules of $ \mathfrak{osp}(1|2)$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909880934203392 |
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| author | Grantcharov, Dimitar Nguyen, Khoa |
| author_facet | Grantcharov, Dimitar Nguyen, Khoa |
| contents | We study properties of two families, $E_{+}(g)$ and $E_-(g)$, of non-weight modules over the orthosymplectic Lie superalgebra $\mathfrak{osp}(1|2)$ that are parameterized by a nonconstant polynomial $g(x) \in \mathbb C [x]$. These families appear naturally from the two oscillator homomorphisms and the exponential modules over the first Weyl algebra $\mathcal D(1)$. We prove simplicity and isomorphism theorems for $E_{+}(g)$ and $E_-(g)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00287 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential modules of $ \mathfrak{osp}(1|2)$ Grantcharov, Dimitar Nguyen, Khoa Representation Theory 17A70, 17B10 We study properties of two families, $E_{+}(g)$ and $E_-(g)$, of non-weight modules over the orthosymplectic Lie superalgebra $\mathfrak{osp}(1|2)$ that are parameterized by a nonconstant polynomial $g(x) \in \mathbb C [x]$. These families appear naturally from the two oscillator homomorphisms and the exponential modules over the first Weyl algebra $\mathcal D(1)$. We prove simplicity and isomorphism theorems for $E_{+}(g)$ and $E_-(g)$. |
| title | Exponential modules of $ \mathfrak{osp}(1|2)$ |
| topic | Representation Theory 17A70, 17B10 |
| url | https://arxiv.org/abs/2511.00287 |