Semisimple coadjoint orbits and cotangent bundles
classification
🧮 math.DG
keywords
orbitsadjointbundlescotangentgeometryhyperbolicproofreal
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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.
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