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In their 1987 paper Kra\'skiewicz and Pragacz defined certain modules, whichwe call KP modules, over the upper triangular Lie algebra whose characters areSchubert polynomials. In a previous work the author showed that the tensorproduct of KP modules always has a KP filtration, i.e. a filtration whose eachsuccessive quotients are isomorphic to KP modules. In this paper we explicitlyconstruct such filtrations for certain special cases of these tensor productmodules, namely $\mathcal{S}_w \otimes S^d(K^i)$ and $\mathcal{S}_w \otimes\bigwedge^d(K^i)$, corresponding to Pieri and dual Pieri rules for Schubertpolynomials.

Kra\'skiewicz-Pragacz modules and Pieri and dual Pieri rules for Schubert polynomials