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
Caviedes Castro, Alexander 1
@article{10_2140_agt_2020_20_565,
author = {Caviedes Castro, Alexander},
title = {Hofer{\textendash}Zehnder capacity and {Bruhat} graph},
journal = {Algebraic and Geometric Topology},
pages = {565--600},
year = {2020},
volume = {20},
number = {2},
doi = {10.2140/agt.2020.20.565},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2020.20.565/}
}
Caviedes Castro, Alexander. Hofer–Zehnder capacity and Bruhat graph. Algebraic and Geometric Topology, Tome 20 (2020) no. 2, pp. 565-600. doi: 10.2140/agt.2020.20.565
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