# Indecomposable $0$-Hecke modules for extended Schur functions

## TL;DR

This paper constructs indecomposable 0-Hecke modules whose quasisymmetric characteristics are the extended Schur functions, providing a new representation-theoretic interpretation of this basis within quasisymmetric functions.

## Contribution

It introduces a novel construction of indecomposable 0-Hecke modules corresponding to extended Schur functions, linking algebraic modules to combinatorial bases.

## Key findings

- Modules are indecomposable.
- Modules' characteristics are extended Schur functions.
- Provides a new representation-theoretic perspective.

## Abstract

The extended Schur functions form a basis of quasisymmetric functions that contains the Schur functions. We provide a representation-theoretic interpretation of this basis by constructing $0$-Hecke modules whose quasisymmetric characteristics are the extended Schur functions. We further prove these modules are indecomposable.