Calculation of j and jm symbols for arbitrary compact groups. I. Methodology

A systematic method is established for computing the coupling coefficients associated with arbitrary compact groups using only the general properties of the coefficients and the specific character theory of the relevant groups. The basic character theory is first outlined. Then a primitive set of 6j symbols is defined and their computation sketched with careful attention being given to matters of phase fixing. A recursive method is developed for calculating arbitrary 6j symbols using the primitive set. Finally, a primitive set of 3jm factors is set up and then the general 3jm factors computed recursively.