# Schubert polynomials as integer point transforms of generalized permutahedra

## TL;DR

This paper demonstrates that Schubert and key polynomials can be represented as positively weighted integer point transforms of generalized permutahedra, linking algebraic combinatorics with geometric structures.

## Contribution

It establishes that the dual character of flagged Weyl modules corresponds to integer point transforms of generalized permutahedra, confirming several recent conjectures.

## Key findings

- Schubert and key polynomials are integer point transforms of generalized permutahedra
- The dual character of flagged Weyl modules has a geometric interpretation
- Several recent conjectures are confirmed by this geometric perspective

## Abstract

We show that the dual character of the flagged Weyl module of any diagram is a positively weighted integer point transform of a generalized permutahedron. In particular, Schubert and key polynomials are positively weighted integer point transforms of generalized permutahedra. This implies several recent conjectures of Monical, Tokcan and Yong.