DUAL MOMENT MAPS INTO LOOP ALGEBRAS

Moment maps are defined from the space of rank-r deformations of a fixed n x n matrix A to the duals {Mathematical expression} of the positive half of the loop algebras {Mathematical expression}. 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 {Mathematical expression} of invariant functions. This gives a dual characterization of integrable Hamiltonian systems as isospectral flow in the two loop algebras. © 1990 Kluwer Academic Publishers.