  The spin one-half Heisenberg chain with $U_q[SU(2)]$ symmetry is studied via
density-matrix renormalization. Ground-state energy and $q$-symmetric
correlation functions are calculated for the non-hermitian case
$q=\exp(i\pi/(r+1))$ with integer $r$. This gives bulk and surface exponents
for (para)fermionic correlations in the related Ising and Potts models. The
case of real $q$ corresponding to a diffusion problem is treated analytically.
