The skew immaculate Hecke poset and 0-Hecke modules

TL;DR

This paper extends the concept of the immaculate Hecke poset to a skew version, exploring its structure and modules for the 0-Hecke algebra, revealing new representation-theoretic insights.

Contribution

Introduction of the skew immaculate Hecke poset and construction of associated modules, expanding understanding of 0-Hecke algebra actions on skew tableaux.

Findings

Skew immaculate Hecke poset structure characterized.

Modules for 0-Hecke algebra on skew tableaux constructed.

Branching rules for skew modules described.

Abstract

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.