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Dual moment maps into loop algebras (1990)

Adams, M. R. ; Harnad, J. ; Hurtubise, J.

Springer

Letters in mathematical physics 20 (1990), S. 299-308

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ISSN: 1573-0530

Keywords: 58F07

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00626526

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