Appears in collection : Reductive groups and automorphic forms. Dedicated to the French school of automorphic forms and in memory of Roger Godement.

In a recent preprint with Sug Woo Shin (https://arxiv.org/abs/1609.04223) I construct Galois representations corresponding for cohomological cuspidal automorphic representations of general symplectic groups over totally real number fields under the local hypothesis that there is a Steinberg component. In this talk I will explain this result and some parts of the construction.