The Gromov width of coadjoint orbits of the symplectic group

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.

18 pages, 2 figures; A mistake (necessary assumption that λis on a rational line) is now corrected. We have also implemented valuable comments of a referee

References in corpus (1)

• Toric degenerations of spherical varieties

Cited by in corpus (3)

• Simplices in Newton-Okounkov bodies and the Gromov width of coadjoint orbits
• The geometric structure of symplectic contraction
• A completely integrable system on $G_2$ coadjoint orbits