Classification of the irreducible ordinary modules for affine vertex operator superalgebras
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918485968289792 |
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| author | Li, Haimin Wang, Qing |
| author_facet | Li, Haimin Wang, Qing |
| contents | Let $\mathfrak{g}$ be a basic classical Lie superalgebra, $\mathcal{k}=\frac{h^{\vee}}{u}-h^{\vee}$ a boundary admissible level of $\widehat{\mathfrak{g}}$, where $u$ is a positive integer and $h^{\vee}$ is the dual Coxeter number of $\mathfrak{g}$. In this paper, we classify the irreducible ordinary modules for the affine vertex operator superalgebra $L_{\widehat{\mathfrak{g}}}(\mathcal{k},0)$ associated to any basic classical Lie superalgebra $\mathfrak{g}$. More specifically, if $\mathfrak{g}$ is a basic classical Lie superalgebra of type I, we prove that $L_{\widehat{\mathfrak{g}}}(\mathcal{k},0)$ has exactly $u$ inequivalent irreducible ordinary modules. If $\mathfrak{g}$ is a finite dimensional simple Lie algebra or a basic classical Lie superalgebra of type II, we prove that $L_{\widehat{\mathfrak{g}}}(\mathcal{k},0)$ itself is the only irreducible ordinary $L_{\widehat{\mathfrak{g}}}(\mathcal{k},0)$-module. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04668 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification of the irreducible ordinary modules for affine vertex operator superalgebras Li, Haimin Wang, Qing Representation Theory Quantum Algebra Let $\mathfrak{g}$ be a basic classical Lie superalgebra, $\mathcal{k}=\frac{h^{\vee}}{u}-h^{\vee}$ a boundary admissible level of $\widehat{\mathfrak{g}}$, where $u$ is a positive integer and $h^{\vee}$ is the dual Coxeter number of $\mathfrak{g}$. In this paper, we classify the irreducible ordinary modules for the affine vertex operator superalgebra $L_{\widehat{\mathfrak{g}}}(\mathcal{k},0)$ associated to any basic classical Lie superalgebra $\mathfrak{g}$. More specifically, if $\mathfrak{g}$ is a basic classical Lie superalgebra of type I, we prove that $L_{\widehat{\mathfrak{g}}}(\mathcal{k},0)$ has exactly $u$ inequivalent irreducible ordinary modules. If $\mathfrak{g}$ is a finite dimensional simple Lie algebra or a basic classical Lie superalgebra of type II, we prove that $L_{\widehat{\mathfrak{g}}}(\mathcal{k},0)$ itself is the only irreducible ordinary $L_{\widehat{\mathfrak{g}}}(\mathcal{k},0)$-module. |
| title | Classification of the irreducible ordinary modules for affine vertex operator superalgebras |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2605.04668 |