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Irreducibility of automorphic Galois representations of G L ( n ) , n at most 5

Frank Calegari, Toby Gee (2013)

Annales de l’institut Fourier

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 .

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