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It is shown that the method of infinitesimal generators ("Racah's method")can be broadly and systematically formulated as a method applicable to thecalculation of reduced coupling coefficients for a generic subalgebra chainG>H, provided the reduced matrix elements of the generators of G and therecoupling coefficients of H are known. The calculation of SO(5)>SO(4) reducedcoupling coefficients is considered as an example, and a procedure fortransformation of reduced coupling coefficients between canonical and physicalsubalegebra chains is presented. The problem of calculating couplingcoefficients for generic irreps of SO(5), reduced with respect to any of itssubalgebra chains, is completely resolved by this approach.

Racah's method for general subalgebra chains: Coupling coefficients of SO(5) in canonical and physical bases