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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.05004 |
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| _version_ | 1866911502693302272 |
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| author | Ayyer, Arvind Prasad, Dipendra |
| author_facet | Ayyer, Arvind Prasad, Dipendra |
| contents | The first part of this paper deals with unipotent and reductive groups over finite fields with $q$ elements in which either $q$ goes to infinity or $G=GL_n(q)$ and $n$ goes to infinity. The second part of the paper deals with the symmetric group $S_n$. The main conclusion that we want to bring out in the case of reductive groups $G(q)$, $q$ varying, is that the dimension data, resp. the size of conjugacy classes, is in a statistical sense, ``roughly'' constant and the same (up to taking the squares). We introduce the notion of {\it asympototically constant}, and {\it asympototically log constant} to make precise these notions, which we apply to various groups discussed in this paper including the symmetric groups $S_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimension statistics of representations of finite groups Ayyer, Arvind Prasad, Dipendra Representation Theory Combinatorics Group Theory 20C30, 20C33, 05A17 The first part of this paper deals with unipotent and reductive groups over finite fields with $q$ elements in which either $q$ goes to infinity or $G=GL_n(q)$ and $n$ goes to infinity. The second part of the paper deals with the symmetric group $S_n$. The main conclusion that we want to bring out in the case of reductive groups $G(q)$, $q$ varying, is that the dimension data, resp. the size of conjugacy classes, is in a statistical sense, ``roughly'' constant and the same (up to taking the squares). We introduce the notion of {\it asympototically constant}, and {\it asympototically log constant} to make precise these notions, which we apply to various groups discussed in this paper including the symmetric groups $S_n$. |
| title | Dimension statistics of representations of finite groups |
| topic | Representation Theory Combinatorics Group Theory 20C30, 20C33, 05A17 |
| url | https://arxiv.org/abs/2512.05004 |