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Generalized MICZ-Kepler Problems and Unitary Highest Weight Modules. E-print

By Guowu Meng


Abstract. 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. 1

Year: 2013
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