Irreducibility of polarized automorphic Galois representations in infinitely many dimensions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911328216547328 |
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| author | Feng, Zachary Whitmore, Dmitri |
| author_facet | Feng, Zachary Whitmore, Dmitri |
| contents | Let $π$ be a polarized, regular algebraic, cuspidal automorphic representation of $\operatorname{GL}_n(\mathbb{A}_F)$ where $F$ is totally real or imaginary CM, and let $(ρ_λ)_λ$ be its associated compatible system of Galois representations. Suppose that $7\nmid n$ and, if $4\mid n$, then $n = 4p$ for some prime number $p$. We prove that there is a Dirichlet density $1$ set of rational primes $\mathcal{L}$ such that whenever $λ\mid \ell$ for some $\ell\in \mathcal{L}$, then $ρ_λ$ is irreducible. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_22631 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irreducibility of polarized automorphic Galois representations in infinitely many dimensions Feng, Zachary Whitmore, Dmitri Number Theory Representation Theory 11F80 (Primary) 11R39, 11F70 (Secondary) Let $π$ be a polarized, regular algebraic, cuspidal automorphic representation of $\operatorname{GL}_n(\mathbb{A}_F)$ where $F$ is totally real or imaginary CM, and let $(ρ_λ)_λ$ be its associated compatible system of Galois representations. Suppose that $7\nmid n$ and, if $4\mid n$, then $n = 4p$ for some prime number $p$. We prove that there is a Dirichlet density $1$ set of rational primes $\mathcal{L}$ such that whenever $λ\mid \ell$ for some $\ell\in \mathcal{L}$, then $ρ_λ$ is irreducible. |
| title | Irreducibility of polarized automorphic Galois representations in infinitely many dimensions |
| topic | Number Theory Representation Theory 11F80 (Primary) 11R39, 11F70 (Secondary) |
| url | https://arxiv.org/abs/2507.22631 |