Dual moment maps into loop algebras |
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| Authors: | M R Adams J Harnad J Hurtubise |
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| Institution: | (1) Department of Mathematics, University of Georgia, 30602 Athens, GA, USA;(2) Centre de Recherches Mathématiques, Université de Montréal, CP 6128-A, H3C 3J7 Montréal, Québec, Canada;(3) Department of Mathematics, Concordia University, Montréal, Québec, Canada;(4) Department of Mathematics, McGill University, H3A 2K6 Montréal, Québec, Canada |
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| Abstract: | Moment maps are defined from the space of rank-r deformations of a fixedn xn matrixA to the duals
of the positive half of the loop algebras
. 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
of invariant functions. This gives a dual characterization of integrable Hamiltonian systems as isospectral flow in the two loop algebras.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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| Keywords: | 58F07 |
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