Semisimple coadjoint orbits and cotangent bundles
arXiv:1408.4693 · doi:10.1112/blms/bdw058
Abstract
Semisimple (co)adjoint orbits through real hyperbolic elements are well-known to be symplectomorphic to cotangent bundles. We provide a new proof of this fact based on elementary results on both Lie theory and symplectic geometry. Our proof establishes a new connection between the Iwasawa horospherical projection and the symplectic geometry of real hyperbolic (co)adjoint orbits.
Abstract and introduction expanded. Bibliography updated. Journal reference added