A superintegrable time-dependent system with kac-moody symmetry

We investigate the Hamiltonian H _KL with a time-dependent potential in N-dimensional space that is a special combination of a Kepler and a harmonic-oscillator potential. The corresponding classical system has an angular-momentum tensor and a time-dependent analog of the Laplace-Runge-Lenz vector, which commute with the “quasi-Hamiltonian” H _c . These quantities are conserved on the orbits of H _KL, and their Poisson brackets yield a realization of twisted or untwisted centerless Kac-Moody algebras of so(N+1). The corresponding quantum-mechanical operators and their commutators yield a representation of the positive subalgebras of the above Kac-Moody algebras.