  Working in light-cone coordinates, we study the zero-modes and the vacuum in
a 2+1 dimensional SU(3) gauge model. Considering the fields as independent of
the tranverse variables, we dimensionally reduce this model to 1+1 dimensions.
After introducing an appropriate su(3) basis and gauge conditions, we extract
an adjoint field from the model. Quantization of this adjoint field and field
equations lead to two constrained and two dynamical zero-modes. We link the
dynamical zero-modes to the vacuum by writing down a Schrodinger equation and
prove the non-degeneracy of the SU(3) vacuum provided that we neglect the
contribution of constrained zero-modes.
