Lie theory and the wave equation in space–time. 3. Semisubgroup coordinates

We classify and study those coordinate systems which permit R separation of variables for the wave equation in four-dimensional space–time and such that at least one of the variables corresponds to a one-parameter symmetry group of the wave equation. We discuss over 100 such systems and relate them to orbits of triplets of commuting operators in the enveloping algebra of the conformal group SO(4,2).