2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120100We observe that the analogue of the Gelfand-Zeitlin action on gl(n,C), which exists on any symplectic manifold M with an Hamiltonian action of GL(n,C), has a natural interpretation as a residual action, after we identify M with a symplectic quotient of the product of M with T*GL(n-1,C)x...xT*GL(1,C). We also show that the Gelfand-Zeitlin actions on T*GL(n,C) and on the regular part of gl(n,C) can be identified with natural Hamiltonian actions on spaces of rational maps into full flag manifolds, while the Gelfand-Zeitlin action on the whole gl(n,C) corresponds to a natural action on a space of rational maps into the manifold of half-full flags in C^{2n}.24 pages; v.2 clarifies a confusing statement in the introductionSymplectic GeometryAlgebraic Geometry53Dxx, 58D15, 14L30, 14R20text