  We study analytically a model where particles with a hard-core repulsion
diffuse on a finite one-dimensional lattice with space-dependent, asymmetric
hopping rates. The system dynamics are given by the
\mbox{U$_{q}$[SU(2)]}-symmetric Hamiltonian of a generalized anisotropic
Heisenberg antiferromagnet. Exploiting this symmetry we derive exact
expressions for various correlation functions. We discuss the density profile
and the two-point function and compute the correlation length $\xi_s$ as well
as the correlation time $\xi_t$. The dynamics of the density and the
correlations are shown to be governed by the energy gaps of a one-particle
system. For large systems $\xi_s$ and $\xi_t$ depend only on the asymmetry. For
small asymmetry one finds $\xi_t \sim \xi_s^2$ indicating a dynamical exponent
$z=2$ as for symmetric diffusion.
