Canonical domains for coadjoint orbits

Abstract

AbstractThis paper describes two real analytic symplectomorphisms defined on appropriate dense open subsets of any coadjoint orbit of a compact semisimple Lie algebra. The first symplectomorphism sends the open dense subset to a bounded subset of a standard cotangent bundle. The second symplectomorphism has as target a bounded subset of a hyperbolic coadjoint orbit of an associated non‐compact semisimple Lie algebra. Therefore, coadjoint orbits of compact Lie algebras are symplectic compactifications of domains of cotangent bundles, and are in symplectic correspondence with hyperbolic orbits of non‐compact semisimple Lie algebras.