## Tewari, Vasu, and van Willigenburg, Stephanie, - Quasisymmetric Schur functions and modules of the $0$-Hecke algebra

dmtcs:2385 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Quasisymmetric Schur functions and modules of the $0$-Hecke algebra

Authors: Tewari, Vasu, and van Willigenburg, Stephanie,

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.

Source : oai:HAL:hal-01207585v1
Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Submitted on: November 21, 2016
Keywords: combinatorial representation theory,$0$-Hecke algebra,composition tableaux,quasisymmetric functions,Schur functions,weak Bruhat order,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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