Super Vust theorem and Schur-Sergeev duality for principal finite $W$-superalgebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866909547962040320 |
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| author | Cheng, Changjie Shu, Bin Zeng, Yang |
| author_facet | Cheng, Changjie Shu, Bin Zeng, Yang |
| contents | Considering the general linear Lie superalgebra $\mathfrak{gl}(m|n)=\mathfrak{gl}(m|n)_{\bar{\bar 0}}\oplus \mathfrak{gl}(m|n)_{\bar{\bar 1}}$ over $\mathbb{C}$, we first formulate a super version of Vust theorem associated with a principal nilpotent element $e\in \mathfrak{gl}(m|n)_{\bar{\bar 0}}$. As an application of this theorem, we then obtain a Schur-Sergeev duality for principal finite $W$-superalgebras which is partially a super version of Brundan-Kleshchev's higher level Schur-Weyl duality established in \cite{BKl} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_11103 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Super Vust theorem and Schur-Sergeev duality for principal finite $W$-superalgebras Cheng, Changjie Shu, Bin Zeng, Yang Representation Theory 17B20, 17B10, 17B08, 81R05 Considering the general linear Lie superalgebra $\mathfrak{gl}(m|n)=\mathfrak{gl}(m|n)_{\bar{\bar 0}}\oplus \mathfrak{gl}(m|n)_{\bar{\bar 1}}$ over $\mathbb{C}$, we first formulate a super version of Vust theorem associated with a principal nilpotent element $e\in \mathfrak{gl}(m|n)_{\bar{\bar 0}}$. As an application of this theorem, we then obtain a Schur-Sergeev duality for principal finite $W$-superalgebras which is partially a super version of Brundan-Kleshchev's higher level Schur-Weyl duality established in \cite{BKl} |
| title | Super Vust theorem and Schur-Sergeev duality for principal finite $W$-superalgebras |
| topic | Representation Theory 17B20, 17B10, 17B08, 81R05 |
| url | https://arxiv.org/abs/2005.11103 |