  We find an exact formula of Gelfand-Kirillov dimensions for the
infinite-dimensional explicit irreducible sl(n, F)-modules that appeared in the
Z^2-graded oscillator generalizations of the classical theorem on harmonic
polynomials established by Luo and Xu. Three infinite subfamilies of these
modules have the minimal Gelfand-Kirillov dimension. They contain weight
modules with unbounded weight multiplicities and completely pointed modules.
