Geodesic
Kraskiewicz-Pragacz modules and Pieri and dual Pieri rules for Schubert polynomials
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020).

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In their 1987 paper Kraskiewicz and Pragacz defined certain modules, 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 Kraskiewicz-Pragacz modules always has 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 Sw Sd(Ki) and Sw Vd(Ki), corresponding to Pieri and dual Pieri rules for Schubert polynomials. 
@article{DMTCS_2020_special_379_a3,
     author = {Watanabe, Masaki},
     title = {Kraskiewicz-Pragacz modules and {Pieri} and dual {Pieri} rules for {Schubert} polynomials},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     year = {2020},
     doi = {10.46298/dmtcs.6321},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6321/}
}
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Watanabe, Masaki. Kraskiewicz-Pragacz modules and Pieri and dual Pieri rules for Schubert polynomials. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi : 10.46298/dmtcs.6321. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6321/

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