J-SYMBOLS AND JM-FACTORS FOR ALL DIHEDRAL AND CYCLIC GROUPS

The methodology of earlier papers by Butler and Wybourne (1976) is used to obtain algebraic formulae for 6j symbols of the double dihedral and cyclic groups and the 3 jm factors for all possible imbeddings: Dm contains/implies Dn and Dm contains/implies Cn. The usual 3 jm symbols of angular momentum theory, that is for SO3 contains/implies SO2, do not have a phase choice which allows their factorisation into SO3 contains/implies Dinfinity and Dinfinity contains/implies SO2 3jm factors. The authors derive the change of phase necessary for factorisation, thus obtaining a relation between SO3 contains/implies Dinfinity factors and the SO3 contains/implies SO2 3jm symbols of standard angular momentum theory. The use of maximal imbeddings has removed the multiplicity problems encountered by other methods.