Hofer-Zehnder capacity and Bruhat graph

TL;DR

This paper establishes bounds for the Hofer-Zehnder capacity of coadjoint orbits of compact Lie groups using Bruhat graph combinatorics, with sharp bounds for unitary groups related to Cayley graph diameters.

Contribution

It introduces a novel combinatorial approach to estimate Hofer-Zehnder capacities via Bruhat graphs, providing sharp bounds for specific cases.

Findings

Bounds for Hofer-Zehnder capacity in terms of Bruhat graph properties

Exact capacity for coadjoint orbits of the unitary group

Capacity bounds match the diameter of weighted Cayley graphs

Abstract

We find bounds for the Hofer-Zehnder capacity of coadjoint orbits of compact Lie groups with respect to the Kostant--Kirillov--Souriau symplectic form in terms of the combinatorics of their Bruhat graph. We show that our bounds are sharp for coadjoint orbits of the unitary group and equal to the diameter of a weighted Cayley graph.