A symplectic approach to van den Ban's convexity theorem

  • Philip Foth

  • Michael Otto

A symplectic approach to van den Ban's convexity theorem cover
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Abstract

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

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Philip Foth, Michael Otto, A symplectic approach to van den Ban's convexity theorem. Doc. Math. 11 (2006), pp. 407–424

DOI 10.4171/DM/216