Prof. Dr. Chun Yin Hui (University of Hongkong )

Given a compatible system {rho_lambda : Gal_K to GL_n(E_lambda)}_lambda of semisimple lambda-adic representations of a number field K satisfying mild local conditions, we prove that for almost all lambda any type A irreducible subrepresentation of rho_lambda otimes overline Q_ell  is residually irreducible.
We apply this result and some potential automorphy theorem to
prove that rho_ lambda otimes overline Q_ell is residually irreducible for
almost all lambda if the compatible system is attached to a regular algebraic, polarized, cuspidal automorphic representation of GL_n(A_Q) and n leq 6.