Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Kraskiewicz-Pragacz modules and Pieri and dual Pieri rules for Schubert polynomials
Masaki Watanabe  1  
1 : Department of Applied Mathematics and Physics [Kyoto]
Graduate School of Informatics Kyoto University 606-8501, Kyoto Japan -  Japon

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.

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