Tensor product of Kraśkiewicz–Pragacz modules

This paper explores further properties of modules related to Schubert polynomials, introduced by Kraśkiewicz and Pragacz. In this paper we show that any tensor product of Kraśkiewicz–Pragacz modules admits a filtration by Kraśkiewicz–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, and gives a new proof to this classical fact.