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arXiv · 1908.07929

Lifting $G$-irreducible but $\mathrm{GL}_n$-reducible Galois representations

Najmuddin Fakhruddin·Chandrashekhar Khare·Stefan Patrikis
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Abstract

In recent work, the authors proved a general result on lifting $G$-irreducible odd Galois representations $\mathrm{Gal}(\overline{F}/F) \to G(\overline{\mathbb{F}}_{\ell})$, with $F$ a totally real number field and $G$ a reductive group, to geometric $\ell$-adic representations. In this note we take $G$ to be a classical group and construct many examples of $G$-irreducible representations to which these new lifting methods apply, but to which the lifting methods provided by potential automorphy theorems do not.

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Najmuddin Fakhruddin, Chandrashekhar Khare, Stefan Patrikis. 2019-08-21. Lifting $G$-irreducible but $\mathrm{GL}_n$-reducible Galois representations. https://arxiv.org/abs/1908.07929

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