  A generalization of the Dirac field equation in three-dimensional Minkowski
space-time to the case of the $\bar{SL}(3,R)$ $\subset$ $\bar{SA}(3,R)$
symmetry is considered. Constraints that ensure a correct physical
interpretation of the corresponding particle states are presented. Dirac-like
equations based on both multiplicity-free and generic infinite-component
$\bar{SL}(3,R)$ representations are outlined.
