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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2510.12496 |
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| _version_ | 1866915554000896000 |
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| author | Dai, Boyi |
| author_facet | Dai, Boyi |
| contents | We study irreducibility of Galois representations $ρ_{π,λ}$ associated to a $n=7$ or 8-dimensional regular algebraic essentially self-dual cuspidal automorphic representation $π$ of $\text{GL}_n(\mathbb{A}_\mathbb{Q})$. We show $ρ_{π,λ}$ is irreducible for all but finitely many $λ$ under the following extra conditions. (i) If $n=7$, and there exists no $λ$ such that the Lie type of $ρ_{π,λ}$ is the standard representation of exceptional group $\textbf{G}_2$. (ii) If $n=8$, and when there exist infinitely many $λ$ such that the Lie type of $ρ_{π,λ}$ is the spin representation of $\text{SO}_7$, we assume there exist no three distinct Hodge-Tate weights form a 3-term arithmetic progression. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12496 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On irreducibility of certain low dimensional automorphic Galois representations Dai, Boyi Number Theory We study irreducibility of Galois representations $ρ_{π,λ}$ associated to a $n=7$ or 8-dimensional regular algebraic essentially self-dual cuspidal automorphic representation $π$ of $\text{GL}_n(\mathbb{A}_\mathbb{Q})$. We show $ρ_{π,λ}$ is irreducible for all but finitely many $λ$ under the following extra conditions. (i) If $n=7$, and there exists no $λ$ such that the Lie type of $ρ_{π,λ}$ is the standard representation of exceptional group $\textbf{G}_2$. (ii) If $n=8$, and when there exist infinitely many $λ$ such that the Lie type of $ρ_{π,λ}$ is the spin representation of $\text{SO}_7$, we assume there exist no three distinct Hodge-Tate weights form a 3-term arithmetic progression. |
| title | On irreducibility of certain low dimensional automorphic Galois representations |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.12496 |