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We observe that the analogue of the Gelfand–Zeitlin action on $${{\mathfrak g \mathfrak l}(n,{\mathbb C})}$$, which exists on any symplectic manifold M with an Hamiltonian action of $${GL(n,{\mathbb C})}$$, has a natural interpretation as a residual action, after we identify M with a symplectic quotient of $${M\times \prod_{i=1}^n T^\ast GL(i,{\mathbb C})}$$. We also show that the Gelfand–Zeitlin actions on $${T^\ast GL(n,{\mathbb C})}$$ and on the regular part of $${{\mathfrak g \mathfrak l}(n,{\mathbb C})}$$ can be identified with natural Hamiltonian actions on spaces of rational maps into full flag manifolds, while the Gelfand–Zeitlin action on the whole $${{\mathfrak g \mathfrak l}(n,{\mathbb C})}$$ corresponds to a natural action on a space of rational maps into the manifold of half-full flags in $${{\mathbb C}^{2n}}$$.

Gelfand–Zeitlin actions and rational maps