## Kraśkiewicz-Pragacz Modules and Pieri and Dual Pieri Rules for Schubert Polynomials

J. Math. Sci. Univ. Tokyo
Vol. 24 (2017), No. 2, Page 259–270.

Watanabe, Masaki
Kraśkiewicz-Pragacz Modules and Pieri and Dual Pieri Rules for Schubert Polynomials
In their 1987 paper Kraśkiewicz and Pragacz defined certain modules $\mathcal{S}_w$ ($w \in S_\infty$), which we call KP modules, over the upper triangular Lie algebra whose characters are Schubert polynomials. In a previous work the author showed that the tensor product of KP modules always has a KP filtration, i.e. a filtration whose each successive quotients are isomorphic to KP modules. In this paper we explicitly construct such filtrations for certain special cases of these tensor product modules, 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 Schubert polynomials.