Non-compact symmetries, extended supergravities and the Wheeler-DeWitt equation

The algebra of local and rigid symmetries of N=16 supergravity in three and two dimensions is considered. The conserved currents of the non-compact rigid E8 and E9 symmetries are explicitly given. On the physical states, the associated charges are found to commute with all local symmetries and, in particular, with the Wheeler-DeWitt hamiltonian. The solutions of the latter are therefore infinitely degenerate. This analysis sheds some new light on the significance of non-compact symmetries in extended supergravities. Furthermore, I argue that E9 plays the role of a 'solution-generating group' for the Wheeler-DeWitt equation of N=16 supergravity in two dimensions, which should thus be completely integrable. (orig.)