  We construct a generalization of the Hasse invariant for certain unitary
Shimura varieties of PEL type whose vanishing locus is the complement of the
so-called \mu-ordinary locus. We show that the \mu-ordinary locus of those
varieties is affine. As an application, we strengthen a special case of a
theorem of one of us (W.G.) on the association of Galois representations to
automorphic representations of unitary groups whose archimedean component is a
holomorphic limit of discrete series.
