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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 withinfinitely many conservation laws and sectors. Simulations show that $C(t)$decays as different powers of $t$, or as $\exp (-t^{1/2})$, depending on thesector. We explain this diversity by relating the problem to diffusion of hardcore particles with conserved spin labels. The model embodies a matrixgeneralization of the Kardar-Parisi-Zhang model of interface roughening. In thesector which includes the empty line, the dynamical exponent $z$ is $2.55 \pm0.15$.Comment: 10 pages, Late

Slow Relaxation in a Model with Many Conservation Laws: Deposition and Evaporation of Trimers on a Line