  We study the slow decay of the steady-state autocorrelation function $C(t)$
in a stochastic model of deposition and evaporation of trimers on a line with
infinitely many conservation laws and sectors. Simulations show that $C(t)$
decays as different powers of $t$, or as $\exp (-t^{1/2})$, depending on the
sector. We explain this diversity by relating the problem to diffusion of hard
core particles with conserved spin labels. The model embodies a matrix
generalization of the Kardar-Parisi-Zhang model of interface roughening. In the
sector which includes the empty line, the dynamical exponent $z$ is $2.55 \pm
0.15$.
