Symplectic capacities of Hermitian symmetric spaces

TL;DR

This paper extends the study of symplectic capacities, specifically Gromov width and Hofer--Zehnder capacity, to Hermitian symmetric spaces of compact type, including Cartan domains and their products.

Contribution

It generalizes previous results from complex Grassmannians to all Hermitian symmetric spaces of compact type and computes capacities for Cartan domains and their products.

Findings

Gromov width and Hofer--Zehnder capacity computed for Cartan domains

Extended Lu's results to broader class of Hermitian symmetric spaces

Provided explicit capacity values for product spaces

Abstract

Inspired by the work of G. Lu on pseudo symplectic capacities we obtain several results on the Gromov width and the Hofer--Zehnder capacity of Hermitian symmetric spaces of compact type. Our results and proofs extend those obtained by Lu for complex Grassmannians to Hermitian symmetric spaces of compact type. We also compute the Gromov width and the Hofer--Zehnder capacity for Cartan domains and their products.