Classifying representations of finite classical groups of Lie type of dimension up to $\ell^4$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917085897031680 |
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| author | Frez, Luis Gutiérrez Zenteno, Adrian |
| author_facet | Frez, Luis Gutiérrez Zenteno, Adrian |
| contents | Let $G$ be a finite classical group of Lie type of rank $\ell$, defined over a field of characteristic $p>2$. In this work, we classify the irreducible representations of $G$ whose dimensions are bounded by a constant proportional to $\ell$, and splits into two cases according to $G$ is of type $A_{\ell}$ or not. Furthermore, we discuss explicit formulas for computing the dimensions of such representations. The motivation for this work arises, in part, from a desire to obtain new results on two classical problems concerning Galois representations: the large image conjecture for automorphic Galois representations and the inverse Galois problem. We conclude the paper by giving some remarks on potential implications in these addresses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classifying representations of finite classical groups of Lie type of dimension up to $\ell^4$ Frez, Luis Gutiérrez Zenteno, Adrian Representation Theory Group Theory Number Theory 20C33, 20G40, 11F80 Let $G$ be a finite classical group of Lie type of rank $\ell$, defined over a field of characteristic $p>2$. In this work, we classify the irreducible representations of $G$ whose dimensions are bounded by a constant proportional to $\ell$, and splits into two cases according to $G$ is of type $A_{\ell}$ or not. Furthermore, we discuss explicit formulas for computing the dimensions of such representations. The motivation for this work arises, in part, from a desire to obtain new results on two classical problems concerning Galois representations: the large image conjecture for automorphic Galois representations and the inverse Galois problem. We conclude the paper by giving some remarks on potential implications in these addresses. |
| title | Classifying representations of finite classical groups of Lie type of dimension up to $\ell^4$ |
| topic | Representation Theory Group Theory Number Theory 20C33, 20G40, 11F80 |
| url | https://arxiv.org/abs/2401.11367 |