$\widetilde{S}_{n}$- and $\overline{S}_{n}$-module structures on $U(\h_n)$

In this paper, we classify the $\widetilde{S}_{n}$- and $\overline{S}_{n}$-modules that are free $U(\h_n)$-modules of rank 1, on which $\widetilde{S}_{n}'$ and $\overline{S}_{n}'$ acts nontrivially, and find the only irreducible submodules of them.