|Date||May 04, 2021|
In this talk, I will explain the construction of the $0$-Hecke module arising from a certain tableau that comes from the Demazure module of type $A$.
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 $0$-Hecke modules whose quasisymmetric characteristics are quasisymmetric Schur functions.