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