Calculation of j and jm symbols for arbitrary compact groups. II. An alternate procedure for angular momentum

The various orthogonality and sum rules which the 6 j and 3 jm symbols satisfy are sufficient to obtain the algebraic formulas for these symbols for SO 3 ⊃ SO 2 . Character theory enters in that the j 's and m 's occurring in the various sums are given by the triangle rule\documentclass{article}\pagestyle{empty}\begin{document}$$ j_1 \times j_2 = \left| {j_1 - j_2 } \right| \oplus \ldots \oplus \left( {j_1 + j_2 } \right) $$\end{document}together with information on the symmetrized product and the branching, SO 3 ⊃ SO 2 ,\documentclass{article}\pagestyle{empty}\begin{document}$$ j \to \left( { - j} \right) \oplus \ldots \oplus \left( j \right) $$\end{document} The resulting calculation is somewhat simpler, algebraically speaking, than previous calculations and has the pedagogical advantage that only the concept of an irreducible representation of a group is required, instead of the more elaborate concept of ladder operators.