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$2n$维的广义 MICZ-Kepler 问题具有$\widetilde{\mr{Spin}}(2, 2n+1)$动力学对称性，该对称性扩展了明显的$\mr{Spin}(2n)$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$\widetilde{\mr{Spin}}(2, 2n+1)$模块，该模块出现在 Enright-Howe-Wallach 分类图中酉最高权模块的第一级约简点。 作为副产品，我们得到了这种酉最高权$\widetilde{\mr{Spin}}(2, 2n+1)$模块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.