On a certain family of U(b)-modules

TL;DR

This paper discusses KP modules related to Schubert polynomials, their filtrations, and applications to positivity in algebraic geometry, highlighting recent results and their implications.

Contribution

It presents new insights into KP modules, their filtrations, and applications to positivity, building on prior work by Kraśkiewicz, Watanabe, and Fulton.

Findings

KP modules realize Schubert polynomials

Filtrations with KP modules as subquotients are studied

Applications to positivity in algebraic geometry are discussed

Abstract

We report on results of Kra\'skiewicz and the author, and Watanabe on KP modules materializing Schubert polynomials, and filtrations having KP modules as their subquotients. We discuss applications of KP filtrations and ample KP bundles to positivity, due respectively to Watanabe and Fulton. The article corresponds to the talk given by the author at the conference "IMPANGA 15" in April 2015.