Filtrations and recursions for Schubert modules

Abstract

Revisiting Kraśkiewicz 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.

39 pages, many figures; v2 adds a positivity conjecture and corrects the functorial definition of flagged Schur modules, along with other minor fixes. To appear in Selecta Mathematica