A symplectic approach to van den Ban's convexity theorem

2005/05/03 by Philip Foth, Michael Otto, Foth, Philip +1
Mathematics · #22E46 #53D17 #53D20 #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:22E46 #msc:53D17 #msc:53D20

paper · pdf · doi:10.48550/arxiv.math/0505063

17 pages

arxiv created 2006/09/25 · arxiv updated 2009/12/01

Abstract

Let G be a complex semisimple Lie group and τa complex antilinear involution that commutes with the Cartan involution. If H denotes the connected subgroup of τ-fixed points in G, and K is maximally compact, each H-orbit in G/K can be equipped with a Poisson structure as described by Evens and Lu. We consider symplectic leaves of certain such H-orbits with a natural hamiltonian torus action. A symplectic convexity theorem of Hilgert-Neeb-Plank then leads to van den Ban's convexity theorem for (complex) semisimple symmetric spaces.

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