Tensor product of Kra\'skiewicz and Pragacz's modules

Abstract

This paper explores further properties of modules related with Schubert polynomials, introduced by Kra\'skiewicz and Pragacz. In this paper we show that any tensor product of Kra\'skiewicz-Pragacz modules admits a filtration by Kra\'skiewicz-Pragacz modules. This result can be seen as a module-theoretic counterpart of a classical result that the product of Schubert polynomials is a positive sum of Schubert polynomials.