Abstract
Moment maps are defined from the space of rank-r deformations of a fixedn xn matrixA to the duals\((\widetilde{g1}(r)^ + )^* , (\widetilde{g1}(n)^ + )^* \) of the positive half of the loop algebras\(\widetilde{g1}(r),\widetilde{g1}(n)\). These maps are shown to give rise to the same invariant manifolds under Hamiltonian flow obtained through the Adler-Kostant-Symes theorem from the rings\(I(\widetilde{g1}(r)^* ),I(\widetilde{g1}(n)^* )\) of invariant functions. This gives a dual characterization of integrable Hamiltonian systems as isospectral flow in the two loop algebras.
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This research partially funded by NSF grant DMS-8601995, U.S. Army grant DAAL03-87-K-0110, and the Natural Sciences and Engineering Research Council of Canada.
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Adams, M.R., Harnad, J. & Hurtubise, J. Dual moment maps into loop algebras. Lett Math Phys 20, 299–308 (1990). https://doi.org/10.1007/BF00626526
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DOI: https://doi.org/10.1007/BF00626526