$0$-Hecke modules for Young row-strict quasisymmetric Schur functions

TL;DR

This paper constructs specific modules of the 0-Hecke algebra that correspond to Young row-strict quasisymmetric Schur functions, providing a new representation-theoretic perspective and classifying their indecomposability.

Contribution

It introduces modules of the 0-Hecke algebra linked to Young row-strict quasisymmetric Schur functions, answering a question of Mason and Niese (2015).

Findings

Modules correspond to Young row-strict quasisymmetric Schur functions.

Provides classification of indecomposable modules.

Establishes a representation-theoretic interpretation of the basis.

Abstract

We construct modules of the $0$-Hecke algebra whose images under the quasisymmetric characteristic map are the Young row-strict quasisymmetric Schur functions. This provides a representation-theoretic interpretation of this basis of quasisymmetric functions, answering a question of Mason and Niese (2015). Additionally, we classify when these modules are indecomposable.