On the one-dimensional representations of finite $W$-superalgebras for $\mathfrak{gl}_{M|N}$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910618361004032 |
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| author | Yang, Fanlei Zeng, Yang |
| author_facet | Yang, Fanlei Zeng, Yang |
| contents | Let $\mathfrak{g}=\mathfrak{gl}_{M|N}(\mathbb{k})$ be the general linear Lie superalgebra over an algebraically closed field $\mathbb{k}$ of characteristic zero. Fix an arbitrary even nilpotent element $e$ in $\mathfrak{g}$ and let $U(\mathfrak{g},e)$ be the finite $W$-superalgebra associated to the pair $(\mathfrak{g},e)$. In this paper we will give a complete classification of one-dimensional representations for $U(\mathfrak{g},e)$. To achieve this, we use the tool of shifted super Yangians to determine the commutative quotients of the finite $W$-superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the one-dimensional representations of finite $W$-superalgebras for $\mathfrak{gl}_{M|N}$ Yang, Fanlei Zeng, Yang Representation Theory Let $\mathfrak{g}=\mathfrak{gl}_{M|N}(\mathbb{k})$ be the general linear Lie superalgebra over an algebraically closed field $\mathbb{k}$ of characteristic zero. Fix an arbitrary even nilpotent element $e$ in $\mathfrak{g}$ and let $U(\mathfrak{g},e)$ be the finite $W$-superalgebra associated to the pair $(\mathfrak{g},e)$. In this paper we will give a complete classification of one-dimensional representations for $U(\mathfrak{g},e)$. To achieve this, we use the tool of shifted super Yangians to determine the commutative quotients of the finite $W$-superalgebras. |
| title | On the one-dimensional representations of finite $W$-superalgebras for $\mathfrak{gl}_{M|N}$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2409.16014 |