Whittaker Modules for W type Cartan Lie superalgebras
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917098479943680 |
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| author | Futorny, Vyacheslav Tantubay, Santanu |
| author_facet | Futorny, Vyacheslav Tantubay, Santanu |
| contents | We consider the category of Whittaker modules for the Lie superalgebra $W_{m,n}$ of vector fields on $\mathbb{C}^{(m|n)}$. For any $\mathbf{a}\in \mathbb{C}^m$ we show the equivalence between the blocks
$Ω_{\mathbf a}^{\widetilde{W}_{m,n}}$ of the category of $(AW)_{m,n}$-Whittaker modules with finite-dimensional Whittaker vector spaces and the category of finite-dimensional modules over certain Lie subsuperalgebra $T_{m,n}$ of $(AW)_{m,n}$ (and also of $\mathfrak{gl}{(m,n)})$. Then we apply the covering technique to study Whittaker $W_{m,n}$-modules and describe simple modules in the category $Ω_{\mathbf a}^{{W}_{m,n}}$ of such modules with finite-dimensional Whittaker vector spaces and with non-singular ${\mathbf a}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17995 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Whittaker Modules for W type Cartan Lie superalgebras Futorny, Vyacheslav Tantubay, Santanu Representation Theory 17B10, 17B15, 17B65, 17B66, 17B68 We consider the category of Whittaker modules for the Lie superalgebra $W_{m,n}$ of vector fields on $\mathbb{C}^{(m|n)}$. For any $\mathbf{a}\in \mathbb{C}^m$ we show the equivalence between the blocks $Ω_{\mathbf a}^{\widetilde{W}_{m,n}}$ of the category of $(AW)_{m,n}$-Whittaker modules with finite-dimensional Whittaker vector spaces and the category of finite-dimensional modules over certain Lie subsuperalgebra $T_{m,n}$ of $(AW)_{m,n}$ (and also of $\mathfrak{gl}{(m,n)})$. Then we apply the covering technique to study Whittaker $W_{m,n}$-modules and describe simple modules in the category $Ω_{\mathbf a}^{{W}_{m,n}}$ of such modules with finite-dimensional Whittaker vector spaces and with non-singular ${\mathbf a}$. |
| title | Whittaker Modules for W type Cartan Lie superalgebras |
| topic | Representation Theory 17B10, 17B15, 17B65, 17B66, 17B68 |
| url | https://arxiv.org/abs/2511.17995 |