Semisimple coadjoint orbits and cotangent bundles
David Mart\'inez Torres
TL;DR
This paper offers a new, elementary proof that semisimple coadjoint orbits through real hyperbolic elements are symplectomorphic to cotangent bundles, linking Lie theory and symplectic geometry.
Contribution
It introduces a novel proof connecting Iwasawa horospherical projection with the symplectic structure of real hyperbolic coadjoint orbits.
Findings
New elementary proof of symplectomorphism
Connection between Iwasawa projection and symplectic geometry
Enhanced understanding of real hyperbolic orbits
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.
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