ON THE DYNAMICAL SYMMETRIES OF THE KEPLER-PROBLEM

We try to understand the geometry of the SO(n + 1,2) action on the Kepler Manifold of the n - dimensional hydrogen atom. We show that the SO(n + 1,2) symmetry of the Kepler Problem is closely related to the fact that the geodesic flow on T*Sn is periodic. We also exhibit the orbit picture analog of the peculiar property of the corresponding SO(n + 1,2) representation; that is, it stays irreducible when restricted to SO(n + 1,1) subgroups. © 1980 American Institute of Physics.