IRREDUCIBILITY OF AUTOMORPHIC GALOIS REPRESENTATIONS OF GL(n), n AT MOST 5. FRANK CALEGARI AND TOBY GEE

Let π be a regular, algebraic, essentially self-dual cuspidal automorphic representation of GLn(AF ), 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.