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Adler-Kostant-Symes systems as Lagrangian gauge theories

L. Feher·A. Gabor
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Abstract

It is well known that the integrable Hamiltonian systems defined by the Adler-Kostant-Symes construction correspond via Hamiltonian reduction to systems on cotangent bundles of Lie groups. Generalizing previous results on Toda systems, here a Lagrangian version of the reduction procedure is exhibited for those cases for which the underlying Lie algebra admits an invariant scalar product. This is achieved by constructing a Lagrangian with gauge symmetry in such a way that, by means of the Dirac algorithm, this Lagrangian reproduces the Adler-Kostant-Symes system whose Hamiltonian is the quadratic form associated with the scalar product on the Lie algebra.

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BibTeXRIS

L. Feher, A. Gabor. 2002-02-22. Adler-Kostant-Symes systems as Lagrangian gauge theories. https://doi.org/10.1016/s0375-9601(02)00978-7

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