SPECIAL SYMMETRIES OF JM-FACTORS AND J-SYMBOLS

It has been suggested that the existence of one-dimensional irreps of a group leads to symmetries in the Racah algebra of the group. The familiar 2jm symbol arises as a special case of these symmetries where the one-dimensional irrep is the identity irrep. The authors derive the general result and give examples for the symmetric groups and for the point groups. These examples show that these new symmetries are more complicated than the previous suggestions imply.