Volume 20, issue 2 (2020)

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Hofer–Zehnder capacity and Bruhat graph

Alexander Caviedes Castro

Algebraic & Geometric Topology 20 (2020) 565–600

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.

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symplectic capacities, coadjoint orbits, Bruhat graph, Hofer–Zehnder capacity
Mathematical Subject Classification 2010
Primary: 14M15, 57R17
Secondary: 53D45
Received: 2 February 2017
Revised: 4 December 2018
Accepted: 19 April 2019
Published: 23 April 2020
Alexander Caviedes Castro
School of Mathematical Sciences
Tel Aviv University
Tel Aviv