Galois representations associated to holomorphic limits of discrete series

We attach Galois representations to automorphic representations on unitary groups whose weight
(=component at infinity) is a holomorphic limit of discrete series. The main innovation is a new
construction of congruences, using the Hasse Invariant, which avoids q-expansions and so is
applicable in much greater generality than previous methods. Our result is a natural
generalization of the classical Deligne-Serre Theorem on weight one modular forms and
work of Taylor on GSp(4).