Distinguished filtrations of the $0$-Hecke modules for dual immaculate
quasisymmetric functions
Distinguished filtrations of the $0$-Hecke modules for dual immaculate
quasisymmetric functions
Let $\alpha$ range over the set of compositions. Dual immaculate quasisymmetric functions $\mathfrak{S}_\alpha^*$, introduced by Berg, Bergeron, Saliola, Serrano, and Zabrocki, provide a quasisymmetric analogue of Schur functions. They also constructed an indecomposable $0$-Hecke module $\mathcal{V}_\alpha$ whose image under the quasisymmetric characteristic is $\mathfrak{S}_\alpha^*$. In this paper, we prove that …