Abstract
In a recent publication, we proposed two possible wave functions for the elementary excitations of the SU(3) Haldane-Shastry model, 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 $\overline{3}$ 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 $\mathrm{SU}(n)$.
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