Geodesic
Quasisymmetric Schur functions and modules of the $0$-Hecke algebra
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014).

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We define a $0$-Hecke action on composition tableaux, and then use it to derive $0$-Hecke modules whose quasisymmetric characteristic is a quasisymmetric Schur function. We then relate the modules to the weak Bruhat order and use them to derive a new basis for quasisymmetric functions. We also classify those modules that are tableau-cyclic and likewise indecomposable. Finally, we develop a restriction rule that reflects the coproduct of quasisymmetric Schur functions. 
@article{DMTCS_2014_special_265_a10,
     author = {Tewari, Vasu and van Willigenburg, Stephanie},
     title = {Quasisymmetric {Schur} functions and modules of the $0${-Hecke} algebra},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)},
     year = {2014},
     doi = {10.46298/dmtcs.2385},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2385/}
}
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Tewari, Vasu; van Willigenburg, Stephanie. Quasisymmetric Schur functions and modules of the $0$-Hecke algebra. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014). doi : 10.46298/dmtcs.2385. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2385/

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