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arXiv · 2603.19768

Irreducibility and Monodromy of Automorphic Galois Representations of $\mathrm{GL}(4)$

Alireza Shavali
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Abstract

We prove that over totally real fields, the $p$-adic Galois representations attached to non-self-dual regular algebraic cuspidal automorphic representations of $\mathrm{GL}(4)$ are irreducible. We then develop the theory of extra-twists in a general setting and use it to compute the monodromy group (over $\mathbb{Q}$) of these Galois representations, in both self-dual and non-self-dual settings, and prove $p$-adic and residual big image results.

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Alireza Shavali. 2026-03-20. Irreducibility and Monodromy of Automorphic Galois Representations of $\mathrm{GL}(4)$. https://arxiv.org/abs/2603.19768

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