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Abstract
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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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Keywords
symplectic capacities, coadjoint orbits, Bruhat graph,
Hofer–Zehnder capacity
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Mathematical Subject Classification 2010
Primary: 14M15, 57R17
Secondary: 53D45
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Publication
Received: 2 February 2017
Revised: 4 December 2018
Accepted: 19 April 2019
Published: 23 April 2020
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