Generalized MICZ-Kepler Problems and Unitary Highest Weight Modules -- II

Details Generalized MICZ-Kepler Problems and Unitary Highest Weight Modules -- II Generalized MICZ-Kepler Problems and Unitary Highest Weight Modules -- II

2007-04-23

arxiv.org/abs/0704.2936v3

J. London Math. Soc. 2010 81(3): 663-678

Physics

Mathematical Physics

16 pages, minor modifications

Scientific paper

For each integer $n\ge 2$, we demonstrate that a 2n-dimensional generalized MICZ-Kepler problem has an $\widetilde{\mr{Spin}}(2, 2n+1)$ dynamical symmetry which extends the manifest $\mr{Spin}(2n)$ symmetry. The Hilbert space of bound states is shown to form a unitary highest weight $\widetilde{\mr{Spin}}(2, 2n+1)$-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 $\widetilde{\mr{Spin}}(2, 2n+1)$-module.

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