Geodesic
A symplectic approach to van den Ban's convexity theorem
Documenta mathematica, Tome 11 (2006), pp. 407-424.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $G$ be a complex semisimple Lie group and $\tau$ a complex antilinear involution that commutes with a Cartan involution. If $H$ denotes the connected subgroup of $\tau$-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.
Classification : 53D17, 53D20, 22E46
Keywords: Lie group, real form, Poisson manifold, symplectic leaf, moment map, convex cone 
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     title = {A symplectic approach to van den {Ban's} convexity theorem},
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Foth, Philip; Otto, Michael. A symplectic approach to van den Ban's convexity theorem. Documenta mathematica, Tome 11 (2006), pp. 407-424. http://geodesic.mathdoc.fr/item/DOCMA_2006__11__a3/