Hofer–Zehnder capacity and Bruhat graph

Caviedes Castro, Alexander

doi:10.2140/agt.2020.20.565

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Hofer–Zehnder capacity and Bruhat graph

Alexander Caviedes Castro

Algebraic & Geometric Topology 20 (2020) 565–600

DOI: 10.2140/agt.2020.20.565

Abstract

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

Keywords

symplectic capacities, coadjoint orbits, Bruhat graph, Hofer–Zehnder capacity

Mathematical Subject Classification 2010

Primary: 14M15, 57R17

Secondary: 53D45

References

Publication

Received: 2 February 2017

Revised: 4 December 2018

Accepted: 19 April 2019

Published: 23 April 2020

Authors

Alexander Caviedes Castro
School of Mathematical Sciences Tel Aviv University Tel Aviv Israel

Volume 20, issue 2 (2020)