ar X iv : 0 70 4 . 29 36 v 3 [ m at h - ph ] 9 A ug 2 00 7 GENERALIZED MICZ - KEPLER PROBLEMS AND UNITARY HIGHEST WEIGHT MODULES – II

For each integer n ≥ 2, we demonstrate that a 2n-dimensional generalized MICZ-Kepler problem has an g 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 g Spin(2, 2n+1)-module which occurs at the first reduction point in the Enright-Howe-Wallach classification diagram for the unitary highest weight modules. As a byproduct, we get a simple geometric realization for such a unitary highest weight g Spin(2, 2n+1)module.