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arXiv · 2408.16694

Filtrations and recursions for Schubert modules

David Anderson
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Abstract

Revisiting Kra\'skiewicz and Pragacz's construction of Schubert modules, we provide a new proof that their characters are equal to Schubert polynomials. The main innovation is a representation-theoretic interpretation of a recurrence relation for Schubert polynomials recently discovered by Nadeau, Spink, and Tewari. Along the way, we review several related constructions, and show that the Nadeau-Spink-Tewari recursion determines the characters of flagged Schur modules coming from the broader classes of "transparent" and "translucent" diagrams. We conclude with a conjecture concerning the Schubert positivity of the characters of transparent diagrams.

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David Anderson. 2024-08-29. Filtrations and recursions for Schubert modules. https://arxiv.org/abs/2408.16694

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