Irreducibility of automorphic Galois representations of , at most
Let be a regular, algebraic, essentially self-dual cuspidal automorphic representation of , where is a totally real field and is at most . We show that for all primes , the -adic Galois representations associated to are irreducible, and for all but finitely many primes , the mod Galois representations associated to are also irreducible. We also show that the Lie algebras of the Zariski closures of the -adic representations are independent of .