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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.11403 |
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| _version_ | 1866912377470976000 |
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| author | Wang, Qiutong |
| author_facet | Wang, Qiutong |
| contents | Let $G$ be a general linear group over $\BR$, $\BC$, or $\BH$, or a real unitary group. In this paper, we precisely describe the number of isomorphism classes of irreducible Casselman-Wallach representations of $G$ with a given infinitesimal character and a given associated variety, expressed in terms of certain combinatorial data called painted Young diagrams and assigned Young diagrams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11403 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting irreducible representations of general linear groups and unitary groups Wang, Qiutong Representation Theory Let $G$ be a general linear group over $\BR$, $\BC$, or $\BH$, or a real unitary group. In this paper, we precisely describe the number of isomorphism classes of irreducible Casselman-Wallach representations of $G$ with a given infinitesimal character and a given associated variety, expressed in terms of certain combinatorial data called painted Young diagrams and assigned Young diagrams. |
| title | Counting irreducible representations of general linear groups and unitary groups |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2504.11403 |