  The $\Gamma$-colored $d$-complete and $\Gamma$-colored minuscule posets unify
and generalize multiple classes of colored posets defined by R.A. Proctor, J.R.
Stembridge, and R.M. Green. In previous work, we showed that $\Gamma$-colored
minuscule posets are necessary and sufficient to build from colored posets
certain representations of Kac--Moody algebras that generalize minuscule
representations of semisimple Lie algebras. In this paper we classify
$\Gamma$-colored minuscule posets, which also classifies the corresponding
representations. We show that $\Gamma$-colored minuscule posets are precisely
disjoint unions of colored minuscule posets of Proctor and connected full heaps
of Green.
