We conjecture that the space of super harmonics has a positive expansion in terms of Hall-Littlewood symmetric functions twisted with a sign character and an expansion in terms of $\omega C_{\alpha}[X;1/q]$ functions with $2^{n−1}$ terms. I will give an introduction to Garnir polynomials and "higher Specht polynomials" and their relation to Hall-Littlewood symmetric functions (see "On certain spaces of Harmonic Polynomials" N. Bergeron and Garsia and "Higher Specht polynomials for the symmetric group" by Terasoma and Yamada) so that hopefully we can exhibit this decomposition explicitly.