标题： 广义MICZ-开普勒问题与单位最高权模——II 显示英文标题

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

摘要： 对于每个整数$n\ge 2$，我们证明一个2n维广义MICZ-开普勒问题具有一个$\widetilde{\mr{Spin}}(2, 2n+1)$动力学对称性，该对称性扩展了显式的$\mr{Spin}(2n)$对称性。 束缚态的希尔伯特空间被证明形成一个酉的最高权$\widetilde{\mr{Spin}}(2, 2n+1)$-模，该模出现在Enright-Howe-Wallach分类图中酉的最高权模的第一个约简点。 作为副产品，我们得到了这种酉的最高权$\widetilde{\mr{Spin}}(2, 2n+1)$-模的一个简单的几何实现。 显示英文摘要

摘要： 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.