In this talk, I will explain the construction of the $$extract_itex$$0$$/extract_itex$$-Hecke module arising from a certain tableau that comes from the Demazure module of type $$extract_itex$$A$$/extract_itex$$.

More precisely, I first give Mason's tableau model of Demazure atoms as a component of the decomposition of the Demazure module.

And then, a basis of the ring of quasisymmetric functions, called quasisymmetric Schur functions, defined by using this model will be presented.

Finally, I will describe the action of the 0-Hecke algebra due to Tewari and van Willigenberg, and describe the $$extract_itex$$0$$/extract_itex$$-Hecke modules whose quasisymmetric characteristics are quasisymmetric Schur functions.