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

Frank Calegari, Toby Gee

Published 2011-04-26, updated 2016-10-10Version 2

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.