The skew immaculate Hecke poset and 0-Hecke modules

The immaculate Hecke poset was introduced and investigated by Niese, Sundaram, van Willigenburg, Vega and Wang, who established the full poset structure, and determined modules for the 0-Hecke algebra action on immaculate and row-strict immaculate tableaux. In this paper, we extend their results by introducing the skew immaculate Hecke poset. We investigate the poset structure, and construct modules for the 0-Hecke algebra action on skew immaculate and skew row-strict immaculate tableaux, thus showing that the skew immaculate Hecke poset captures representation-theoretic information analogous to the immaculate Hecke poset. We also describe branching rules for the resulting skew modules.