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Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2020

Kraskiewicz-Pragacz modules and Pieri and dual Pieri rules for Schubert polynomials

Résumé

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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Dates et versions

hal-02168180 , version 1 (28-06-2019)

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Masaki Watanabe. Kraskiewicz-Pragacz modules and Pieri and dual Pieri rules for Schubert polynomials. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6321⟩. ⟨hal-02168180⟩
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