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

Abstract

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.

16 pages, minor modifications

References in corpus (4)

• The MICZ-Kepler Problems in All Dimensions
• Dirac and Yang Monopoles Revisited
• Generalized MICZ-Kepler Problems and Unitary Highest Weight Modules
• Generalized Dirac monopoles in non-Abelian Kaluza-Klein theories

Cited by in corpus (11)

• Euclidean Jordan Algebras, Hidden Actions, and $J$-Kepler Problems
• Generalized MICZ-Kepler Problems and Unitary Highest Weight Modules
• The Sp(1)-Kepler Problems
• The O(1)-Kepler Problems
• The U(1)-Kepler Problems
• The classical dynamic symmetry for the $\mathrm{Sp}(1)$-Kepler problems
• Perturbed $(2n-1)$-Dimensional Kepler Problem and the Nilpotent Adjoint Orbits of $U(n,n)$
• The classical dynamic symmetry for the $\mathrm{U}(1)$-Kepler problems
• A characterization of the unitary highest weight modules by Euclidean Jordan algebras
• Families of Symmetries and the Hydrogen Atom
• Algebraic structure underlying spherical, parabolic and prolate spheroidal bases of the nine-dimensional MICZ-Kepler problem