An explicit characterization of socular simple modules of $\mathfrak{sl}(n,\mathbb{C})$
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929383655079936 |
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| author | Bai, Zhanqiang Xiao, Wei Xie, Xun |
| author_facet | Bai, Zhanqiang Xiao, Wei Xie, Xun |
| contents | Let $\mathfrak{g}$ be a simple complex Lie algebra with a Cartan subalgebra $\mathfrak{h}$. We fix a standard parabolic subalgebra $\mathfrak{p}\supset \mathfrak{h}$. The socular simple modules play an important role in the parabolic versions of category $\mathcal{O}^{\mathfrak{p}}$. From Irving's work, we know that these modules are just those modules with largest possible Gelfand-Kirillov dimension in $\mathcal{O}^{\mathfrak{p}}$. In this article, we will give an explicit characterization for these modules of $\mathfrak{sl}(n,\mathbb{C})$. Our characterization is given in the information of the corresponding highest weight and Young tableau. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_05422 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An explicit characterization of socular simple modules of $\mathfrak{sl}(n,\mathbb{C})$ Bai, Zhanqiang Xiao, Wei Xie, Xun Representation Theory Let $\mathfrak{g}$ be a simple complex Lie algebra with a Cartan subalgebra $\mathfrak{h}$. We fix a standard parabolic subalgebra $\mathfrak{p}\supset \mathfrak{h}$. The socular simple modules play an important role in the parabolic versions of category $\mathcal{O}^{\mathfrak{p}}$. From Irving's work, we know that these modules are just those modules with largest possible Gelfand-Kirillov dimension in $\mathcal{O}^{\mathfrak{p}}$. In this article, we will give an explicit characterization for these modules of $\mathfrak{sl}(n,\mathbb{C})$. Our characterization is given in the information of the corresponding highest weight and Young tableau. |
| title | An explicit characterization of socular simple modules of $\mathfrak{sl}(n,\mathbb{C})$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2301.05422 |