Resumen de Generalized MICZ�Kepler problems and unitary highest weight modules, II

Guowu Meng

• For each integer n  2, we demonstrate that a 2n-dimensional generalized MICZ�Kepler problem has a Spin(2, 2n + 1) dynamical symmetry which extends the manifest Spin(2n) symmetry. The Hilbert space of bound states is shown to form a unitary highest weight Spin(2, 2n + 1)-module with the minimal positive Gelfand�Kirillov dimension. As a byproduct, we get a simple geometric realization for such a unitary highest weight Spin(2, 2n + 1)-module.