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Quasisymmetric Schur functions and modules of the $0$-Hecke algebra

Abstract : 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.
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Vasu Tewari, Stephanie van Willigenburg. Quasisymmetric Schur functions and modules of the $0$-Hecke algebra. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.113-124. ⟨hal-01207585⟩

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