Geodesic
A symplectic approach to van den Ban's convexity theorem
Documenta mathematica, Tome 11 (2006), pp. 407-424
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Let G be a complex semisimple Lie group and τ a complex antilinear involution that commutes with a 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 then leads to van den Ban's convexity result for (complex) semisimple symmetric spaces.
DOI : 10.4171/dm/216
Classification : 22E46, 53D17, 53D20
Mots-clés : moment map, Lie group, real form, Poisson manifold, symplectic leaf, convex cone 
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     author = {Philip Foth and Michael Otto},
     title = {A symplectic approach to van den {Ban's} convexity theorem},
     journal = {Documenta mathematica},
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     year = {2006},
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     doi = {10.4171/dm/216},
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Philip Foth; Michael Otto. A symplectic approach to van den Ban's convexity theorem. Documenta mathematica, Tome 11 (2006), pp. 407-424. doi: 10.4171/dm/216

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