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Gelfand-Zeitlin actions and rational maps

Authors
  • Bielawski, Roger
  • Pidstrygach, Victor
Type
Preprint
Publication Date
Dec 16, 2006
Submission Date
Dec 13, 2006
Identifiers
arXiv ID: math/0612365
Source
arXiv
License
Unknown
External links

Abstract

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}.

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