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Let pi be a regular, algebraic, essentially self-dual cuspidal automorphicrepresentation of GL_n(A_F), where F is a totally real field and n is at most5. We show that for all primes l, the l-adic Galois representations associatedto pi are irreducible, and for all but finitely many primes l, the mod l Galoisrepresentations associated to pi are also irreducible. We also show that theLie algebras of the Zariski closures of the l-adic representations areindependent of l.

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