Unisingular representations of rank 1 finite simple groups of Lie type
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917099643863040 |
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| author | Pellegrini, Marco Antonio Schena, Lorenzo |
| author_facet | Pellegrini, Marco Antonio Schena, Lorenzo |
| contents | A representation $Φ: G \to \mathrm{GL}_n(\mathbb{F})$ of a finite group $G$ is called unisingular if the matrix $Φ(g)$ admits $1$ as an eigenvalue for any $g\in G$. In this paper, we determine all the complex irreducible unisingular representations of the finite simple groups of Lie type of rank $1$ and of the almost simple sporadic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05164 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unisingular representations of rank 1 finite simple groups of Lie type Pellegrini, Marco Antonio Schena, Lorenzo Group Theory 20C15, 20C33, 20C34 A representation $Φ: G \to \mathrm{GL}_n(\mathbb{F})$ of a finite group $G$ is called unisingular if the matrix $Φ(g)$ admits $1$ as an eigenvalue for any $g\in G$. In this paper, we determine all the complex irreducible unisingular representations of the finite simple groups of Lie type of rank $1$ and of the almost simple sporadic groups. |
| title | Unisingular representations of rank 1 finite simple groups of Lie type |
| topic | Group Theory 20C15, 20C33, 20C34 |
| url | https://arxiv.org/abs/2511.05164 |