Resumen
The standard Poisson structures on the flag varieties $G/P$ of a complex reductive algebraic group $G$ are investigated. It is shown that the orbits of symplectic leaves in $G/P$ under a fixed maximal torus of $G$ are smooth irreducible locally closed subvarieties of $G/P$, isomorphic to intersections of dual Schubert cells in the full flag variety $G/B$ of $G$, and their Zariski closures are explicitly computed. Two different proofs of the former result are presented. The first is in the framework of Poisson homogeneous spaces, and the second one uses an idea of weak splittings of surjective Poisson submersions, based on the notion of Poisson--Dirac submanifolds. For a parabolic subgroup $P$ with abelian...