%0 Journal Article
%T Gelfand-Zeitlin actions and rational maps
%A Roger Bielawski
%A Victor Pidstrygach
%J Mathematics
%D 2006
%I arXiv
%X We 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}.
%U http://arxiv.org/abs/math/0612365v2