On hidden couplings and relationships in the angular momentum theory

Problem of finding hidden couplings and relationships, which are not given by the usual theory of angular momentum, is considered. To this end, the general method of constructing generating invariants for all generalized Klebsch-Gordan coefficients, including arbitrary number of spinors, is developed. Concrete expressions for these generating invariants are derived and analysed. The ways of obtaining new relationships and generalizing the present theory of angular momentum are pointed out. Possibilities of various applications of the methods developed are discussed