  This paper proves that the nearby cycles complexes on a certain family of PEL
local models are central with respect to the convolution product of sheaves on
the corresponding affine flag varieties. As a corollary, the semisimple trace
functions defined using the action of Frobenius on those nearby cycles
complexes are, via the sheaf-function dictionary, in the centers of the
corresponding Iwahori-Hecke algebras. This is commonly referred to as
Kottwitz's Conjecture. The reductive groups associated to the PEL local models
under consideration are unramified unitary similitude groups with even
dimension. The proof follows the method of Haines-Ngo 2002. Upon completion of
the first version of this paper, Pappas and Zhu released a preprint, now
published, which contained within its scope the main theorem of this paper.
However, the methods of Pappas-Zhu are very different and some of the proofs
from this paper have been useful in forthcoming work of Haines-Stroh.
