Irreducibility of automorphic Galois representations of GL(n), n at most 5
Annales de l'Institut Fourier, Volume 63 (2013) no. 5, pp. 1881-1912.

Let π be a regular, algebraic, essentially self-dual cuspidal automorphic representation of GL n (𝔸 F ), where F is a totally real field and n is at most 5. We show that for all primes l, the l-adic Galois representations associated to π are irreducible, and for all but finitely many primes l, the mod l Galois representations associated to π are also irreducible. We also show that the Lie algebras of the Zariski closures of the l-adic representations are independent of l.

Nous prouvons l’irréductibilité pour n inférieur ou égal à 5 des représentations galoisiennes l-adiques associées aux représentations automorphes cuspidales algébriques et régulières de GL n sur un corps totalement réel qui sont autoduales à torsion près. Nous prouvons également l’irréductibilité des représentations galoisiennes modulo l pour presque tout l, et nous montrons l’indépendance en l de l’algèbre de Lie de la clôture Zariskienne de la représentation l-adique.

DOI: 10.5802/aif.2817
Classification: 11F80, 11R39
Keywords: Galois representations, automorphic representations, représentations galoisiennes, représentations automorphes
Calegari, Frank 1; Gee, Toby 1

1 Northwestern University Department of Mathematics 2033 Sheridan Road Evanston IL 60208-2730 (USA)
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     title = {Irreducibility of automorphic {Galois} representations of $GL(n)$, $n$ at most $5$},
     journal = {Annales de l'Institut Fourier},
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Calegari, Frank; Gee, Toby. Irreducibility of automorphic Galois representations of $GL(n)$, $n$ at most $5$. Annales de l'Institut Fourier, Volume 63 (2013) no. 5, pp. 1881-1912. doi : 10.5802/aif.2817. http://www.numdam.org/articles/10.5802/aif.2817/

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