Whittaker modules over the loop Virasoro algebra
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918150511001600 |
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| author | Li, Zhiqiang Tan, Shaobin Wang, Qing |
| author_facet | Li, Zhiqiang Tan, Shaobin Wang, Qing |
| contents | In this paper, we first study two classes of Whittaker modules over the loop Witt algebra ${\mathfrak g}:=\mathcal{W}\otimes\mathcal{A}$, where $\mathcal{W}=\text{Der}({\mathbb{C}}[t])$, $\mathcal{A}={\mathbb{C}}[t,t^{-1}]$. The necessary and sufficient conditions for these Whittaker modules being simple are determined. Furthermore, we study a family of Whittaker modules over the loop Virasoro algebra $\mathfrak{L}:=Vir\otimes\mathcal{A}$, where $Vir$ is the Virasoro algebra. The irreducibility criterion for these Whittaker modules are obtained. As an application, we give the irreducibility criterion for universal Whittaker modules of the affine Lie algebra $\widehat{\mathfrak{sl}_{2}}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_24574 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Whittaker modules over the loop Virasoro algebra Li, Zhiqiang Tan, Shaobin Wang, Qing Representation Theory Quantum Algebra In this paper, we first study two classes of Whittaker modules over the loop Witt algebra ${\mathfrak g}:=\mathcal{W}\otimes\mathcal{A}$, where $\mathcal{W}=\text{Der}({\mathbb{C}}[t])$, $\mathcal{A}={\mathbb{C}}[t,t^{-1}]$. The necessary and sufficient conditions for these Whittaker modules being simple are determined. Furthermore, we study a family of Whittaker modules over the loop Virasoro algebra $\mathfrak{L}:=Vir\otimes\mathcal{A}$, where $Vir$ is the Virasoro algebra. The irreducibility criterion for these Whittaker modules are obtained. As an application, we give the irreducibility criterion for universal Whittaker modules of the affine Lie algebra $\widehat{\mathfrak{sl}_{2}}$. |
| title | Whittaker modules over the loop Virasoro algebra |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2509.24574 |