The forms of the new operators made apparent the fact that the basis states of an irreducible representation of SU(3)are linear combinations of the CG series of SU(2) with the same value of j, m and j1 – j2. Obtaining the SU(2) basis for SU(3) was thereby shown to be closely related to the theory of coupling of two angular momenta. The basic states of SU(3) were later used in deriving the matrix elements of finite transformations of SU(3). Simple analytic continuation of Majumdar's generating function of the SU(2) CGC was later understood to be the 'master function' for the solution of several problems of non-compact groups such as SU(1,1) and SL(2,C). The interpretation and domain of the complex variables, however, change from case to case. For example, in the representation theory of SL(2,C) these represent a pair of complex numbers i.e. spinors transforming according to the fundamental representation of SL(2,C) and the complex conjugate respectively. On the other hand, for the CG problem of SU(1,1), they transform according to two distinct SU(1,1) groups.