Letters in Mathematical Physics

, Volume 20, Issue 4, pp 299–308 | Cite as

Dual moment maps into loop algebras

  • M. R. Adams
  • J. Harnad
  • J. Hurtubise
Article

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.

AMS subject classification (1980)

58F07 

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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • M. R. Adams
    • 1
  • J. Harnad
    • 2
    • 3
  • J. Hurtubise
    • 4
  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA
  2. 2.Centre de Recherches MathématiquesUniversité de MontréalMontréalCanada
  3. 3.Department of MathematicsConcordia UniversityMontréalCanada
  4. 4.Department of MathematicsMcGill UniversityMontréalCanada

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