SYMMETRIES OF THE EINSTEIN HAMILTONIAN

The vacuum Einstein equations for metrics that have two commuting spac elike Killing vector fields are studied from a Hamiltonian point of vi ew using the Ashtekar variables. It is shown that the evolution equati ons are equivalent to those of a modified SL(2) principal chiral model with a time dependent 'coupling constant'. This fact is used to extra ct an infinite set of symmetries of the Einstein Hamiltonian via a gen eralized zero-curvature formulation. These symmetries give evolving ob servables explicitly on the phase space, and may be viewed as providin g an infinite set of solutions of the Hamiltonian Einstein equations. The possibility of quantization using these observables is briefly dis cussed.