  We study the quantum dynamics of a one-dimensional SU(3)-symmetric system of
cold atoms in the presence of two-body losses. We exploit the representation
theory of SU(3), the so-called eightfold way, as a scheme to organize the dark
states of the dissipative dynamics in terms of generalized Dicke states and
show how they are dynamically approached, both in the weakly- and and
strongly-interacting and dissipative regimes. Our results are relevant for a
wide class of alkaline-earth(-like) gases experiments, paving the way to the
dissipative preparation and exploitation of generalized Dicke states.
