  The supersingular locus in the fiber at p of a Shimura variety attached to a
unitary similitude group GU(1,n-1) over Q is uniformized by a formal scheme
\Cal N. In the case when p is inert, we define special cycles Z(x) in \Cal N,
associated to a collection x of m `special homomorphisms' with fundamental
matrix T in Herm_m(OK). When m=n and T is nonsingular, we show that the cycle
Z(x) is a union of components of the Ekedahl-Oort stratification, and we give a
necessary and sufficient conditions, in terms of T, for Z(x) to be irreducible.
When Z(x) is zero dimensional -- in which case it reduces to a single point --
we determine the length of the corresponding local ring by using a variant of
the theory of quasi-canonical liftings. We show that this length coincides with
the derivative of a representation density for hermitian forms.
