HIGHER HAMILTONIAN STRUCTURES (THE SL2 CASE)

The procedure of Magri and Weinstein is applied to produce an infinity of compatible Poisson structures on a bihamiltonian manifold, to the case of the KdV phase space. The higher Gel'fand-Dikii structures thus obtained contain nonlocal terms which are expressed with the help of the r.h.s. of the KdV hierarchy. A generating function for all these P oisson structures is given in terms of the Baker-Akhiezer functions. T he symplectic leaves of these Poisson structures are described.