Nikolaus Conference 2015     

For the study of quantum-mechanical systems of high symmetry, group-subgroup chains are of great importance in the specification of good quantum numbers and practical bases for the system's Hilbert space. This specification may be aided by determining the invariants of a group with respect to the subgroup. We develop a graphical means for doing this, and apply it to the cases \(SO(5)\supset SO(3)\) and \(SU(4)\supset SU(2)\times SU(2)\), the results of which are utilized in nuclear physics and quantum computing. Finally, we report on progress in the analogous but more difficult case of \(SO(7)\supset SO(3)\), which is also of use in nuclear physics.