Companion forms for unitary and symplectic groups

Abstract

We prove a companion forms theorem for ordinary $n$-dimensional automorphic Galois representations, by use of automorphy lifting theorems developed by the second author and a technique for deducing companion forms theorems developed by the first author. We deduce results about the possible Serre weights of $modl$ Galois representations corresponding to automorphic representations on unitary groups. We then use functoriality to prove similar results for automorphic representations of ${GSp}_4$ over totally real fields.