The Gromov width of coadjoint orbits of the symplectic group

TL;DR

This paper determines the exact Gromov width of coadjoint orbits of the symplectic group by using toric degenerations and string polytopes, confirming previous upper bounds.

Contribution

It establishes the precise Gromov width of these orbits, advancing understanding of symplectic geometry and representation theory.

Findings

Gromov width equals the previously known upper bound

Uses toric degeneration to relate coadjoint orbits to toric varieties

Connects symplectic geometry with crystal basis combinatorics

Abstract

We prove that the Gromov width of coadjoint orbits of the symplectic group is at least equal to the upper bound known from the works of Zoghi and Caviedes. This establishes the actual Gromov width. Our work relies on a toric degeneration of a coadjoint orbit to a toric variety. The polytope associated to this toric variety is a string polytope arising from a string parametrization of elements of a crystal basis for a certain representation of the symplectic group.