The sparsity of character tables over finite reductive groups and its additive analogue
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909946485932032 |
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| author | Nam, GyeongHyeon Puskás, Anna |
| author_facet | Nam, GyeongHyeon Puskás, Anna |
| contents | We consider the proportion of zero entries in the character table of a sequence of reductive groups over a finite field. We prove an asymptotic lower bound when the reductive group is fixed and the size of the finite field increases. Furthermore, we prove that when considering a sequence of reductive groups with increasing semisimple rank, the proportion is asymptotically one. We also establish an additive analogue of this phenomenon in the context of a fixed reductive Lie algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05773 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The sparsity of character tables over finite reductive groups and its additive analogue Nam, GyeongHyeon Puskás, Anna Representation Theory We consider the proportion of zero entries in the character table of a sequence of reductive groups over a finite field. We prove an asymptotic lower bound when the reductive group is fixed and the size of the finite field increases. Furthermore, we prove that when considering a sequence of reductive groups with increasing semisimple rank, the proportion is asymptotically one. We also establish an additive analogue of this phenomenon in the context of a fixed reductive Lie algebra. |
| title | The sparsity of character tables over finite reductive groups and its additive analogue |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2512.05773 |