We prove a companion forms theorem for ordinary -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 Galois representations corresponding to automorphic representations on unitary groups. We then use functoriality to prove similar results for automorphic representations of over totally real fields.
Toby Gee. David Geraghty. "Companion forms for unitary and symplectic groups." Duke Math. J. 161 (2) 247 - 303, 1 February 2012. https://doi.org/10.1215/00127094-1507376