INTEGRABILITY AND BIHAMILTONIAN STRUCTURE OF THE EVEN ORDER SKdV HIERARCHIES

We study reductions of the even order SKP hierarchy. We prove that these sys-tems are integrable and bihamiltonian. We derive an infinite set of independent polynomial conservation laws, prove their nontriviality, and derive Lenard relations between them. A further reduction of the simplest such hierarchy is identified with the supersymmetric KdV hierarchy of Manin and Radul. We prove that it inherits all the bihamiltonian and integrability properties from the unreduced hierarchy