Simplices in Newton-Okounkov bodies and the Gromov width of coadjoint orbits

TL;DR

This paper proves the conjectured Gromov width for coadjoint orbits of all compact connected simple Lie groups using a unified approach based on analyzing simplices within Newton-Okounkov bodies.

Contribution

It provides a uniform proof for the Gromov width conjecture across all such Lie groups by leveraging Newton-Okounkov body analysis.

Findings

Confirmed the Gromov width conjecture for all compact connected simple Lie groups.

Developed a unified method using simplices in Newton-Okounkov bodies.

Enhanced understanding of symplectic geometry of coadjoint orbits.

Abstract

We give a uniform proof for the conjectured Gromov width of coadjoint orbits of all compact connected simple Lie groups, by analyzing simplices in Newton-Okounkov bodies.