  In a recent publication, we proposed two possible wave functions for the
elementary excitations of the SU(3) Haldane--Shastry model (HSM), but argued on
very general grounds that only one or the other can be a valid excitation. Here
we provide the explicit details of our calculation proving that the wave
function describing a coloron excitation which transforms according to
representation $\bar{3}$ under SU(3) rotations if the spins of the original
model transform according to representation 3, is exact. We further provide an
explicit construction of the exact color-polarized two-coloron eigenstates, and
thereby show that colorons are free but that their relative momentum spacings
are shifted according to fractional statistics with parameter $g=2/3$. We
evaluate the SU(3) spin currents. Finally, we interpret our results within the
framework of the asymptotic Bethe Ansatz and generalize some of them to the
case of SU($n$).
