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