The Gromov width of coadjoint orbits of the symplectic group

2016/01/31 by Iva Halacheva, Milena Pabiniak · 1 citation
Mathematics · #math.SG #msc:53D99

paper · pdf · doi:10.2140/pjm.2018.295.403

published as Pacific J. Math. 295 (2018) 403-420 · 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

arxiv created 2017/08/08 · arxiv updated 2018/04/25

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.

Cited by

• Toric degenerations in symplectic geometry

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