A symplectic approach to van den Ban's convexity theorem
Let be a complex semisimple Lie group and a complex antilinear involution that commutes with a Cartan involution. If denotes the connected subgroup of -fixed points in , and is maximally compact, each -orbit in can be equipped with a Poisson structure as described by Evens and Lu. We consider symplectic leaves of certain such -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.
Cite this article
Philip Foth, Michael Otto, A symplectic approach to van den Ban's convexity theorem. Doc. Math. 11 (2006), pp. 407–424DOI 10.4171/DM/216