We introduce a new basis of quasisymmetric functions, the row-strict dual immaculate functions. We construct a cyclic and indecomposable 0-Hecke algebra module for these functions. Our row-strict immaculate functions are related to the dual immaculate functions of Berg-Bergeron-Saliola-Serrano-Zabrocki by the involution $\psi$ on the ring $Qsym$ of quasisymmetric functions. We give an explicit description of the effect of $\psi$ on the associated 0-Hecke modules, via the poset induced by the 0-Hecke action on standard immaculate tableaux. This remarkable poset reveals other 0-Hecke submodules and quotient modules, often cyclic and indecomposable, notably for a row-strict analogue of the extended Schur functions studied in Assaf-Searles.
This is joint work with Elizabeth Niese, Stephanie van Willigenburg, Julianne Vega and Shiyun Wang.