The dynamical structure factor S(q, omega) of the SU(K) (K = 2, 3, 4) Halda
ne-Shastry model is derived exactly at zero temperature for arbitrary size
of the system. The result is interpreted in terms of free quasi-particles w
hich are generalization of spinons in the SU(2) case; the excited states re
levant to S(q, omega) consist of K quasi-particles each of which is charact
erized by a set of K - 1 quantum numbers. Near the boundaries of the region
where S(q, omega) is nonzero, S(q, omega) shows the power-law singularity.
It is found that the divergent singularity occurs only in the lowest edges
starting from (q, omega) = (0, 0) toward positive and negative q. The anal
ytic result is checked numerically for finite systems via exact diagonaliza
tion and recursion methods.