Hidden couplings and relationships in the theory of angular momenta

We consider the problem of finding hidden couplings and relationships not contained in the existing theory of angular momenta. For this purpose, we develop a general method for constructing generating invariants for all generalized Clebsch–Gordan coefficients that couple an arbitrary number of spinors. We obtain and analyze concrete expressions for such generating invariants. We find from this ways to obtain new relations and ways to generalize the theory of angular momenta. We discuss the possible applications of the method.