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In [5,6] Kraśkiewicz and Pragacz introduced representations of the upper-triangular Lie algebra b whose characters are Schubert polynomials. In [12] the author studied the properties of Kraśkiewicz–Pragacz modules using the theory of highest weight categories. From the results there, in particular we obtain a certain highest weight category whose standard modules are KP modules. In this paper we show...
This paper explores further properties of modules related to Schubert polynomials, introduced by Kraśkiewicz and Pragacz. In this paper we show that any tensor product of Kraśkiewicz–Pragacz modules admits a filtration by Kraśkiewicz–Pragacz modules. This result can be seen as a module-theoretic counterpart of a classical result that the product of Schubert polynomials is a positive sum of Schubert...
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