Geometric Approach to Mirabolic Schur-Weyl Duality of Type A
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914744586207232 |
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| author | Fan, Zhaobing Zhang, Zhicheng Ma, Haitao |
| author_facet | Fan, Zhaobing Zhang, Zhicheng Ma, Haitao |
| contents | We commence by constructing the mirabolic quantum Schur algebra, utilizing the convolution algebra defined on the variety of triples of two $n$-step partial flags and a vector. Subsequently, we employ a stabilization procedure to derive the mirabolic quantum $\mathfrak{gl}_n$. Then we present the geometric approach of the mirabolic Schur-Weyl duality of type $A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05594 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric Approach to Mirabolic Schur-Weyl Duality of Type A Fan, Zhaobing Zhang, Zhicheng Ma, Haitao Representation Theory We commence by constructing the mirabolic quantum Schur algebra, utilizing the convolution algebra defined on the variety of triples of two $n$-step partial flags and a vector. Subsequently, we employ a stabilization procedure to derive the mirabolic quantum $\mathfrak{gl}_n$. Then we present the geometric approach of the mirabolic Schur-Weyl duality of type $A$. |
| title | Geometric Approach to Mirabolic Schur-Weyl Duality of Type A |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2404.05594 |