# Irreducibility of automorphic Galois representations of low dimensions

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## Abstract

Let \(\pi \) be a polarizable, regular algebraic, cuspidal automorphic representation of \(\text { GL }_n(\mathbb {A}_F)\), where *F* is an imaginary CM field and \(n \le 6\). We show that there is a Dirichlet density 1 set \(\mathfrak {L}\) of rational primes, such that for all \(l\in \mathfrak {L}\), the *l*-adic Galois representations associated to \(\pi \) are irreducible.

## Mathematics Subject Classification

11F80 11F22 11F70## Notes

### Acknowledgements

I would like to thank my Ph.D. advisor Richard Taylor for proposing this problem to me and for many helpful discussions during the completion of this manuscript.

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