Gelfand-Kirillov dimensions of the ℤ2-graded oscillator representations of $$\mathfrak{s}\mathfrak{l}$$ (n)

We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible $$\mathfrak{s}\mathfrak{l}$$ (n, $$\mathbb{F}$$ )-modules that appeared in the ℤ2-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.