  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 due to the
first author. We deduce results about the possible Serre weights of mod l
Galois representations corresponding to automorphic representations on unitary
groups. We then use functoriality to prove similar results for automorphic
representations of GSp4 over totally real fields.
