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

Details Irreducibility of automorphic Galois representations of GL(n), n at most 5 Irreducibility of automorphic Galois representations of GL(n), n at most 5

2011-04-26

arxiv.org/abs/1104.4827v1

Mathematics

Number Theory

18 pages

Scientific paper

Let pi 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 pi are irreducible, and for all but finitely many primes l, the mod l Galois representations associated to pi 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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