Restriction of irreducible representations of groups to a subgroup

Abstract

The number and character of the irreducible representations of a subgroup, contained in an irreducible representation of the whole group (if this representation is restricted to the sub­ group) play an important role in quantum mechanics. They give the number and type of the states, generated by a symmetry breaking perturbation, from a state which has the symmetry of the whole group. Three equations are derived here for the number and character of the representations of the subgroup, resulting from the restriction of the irreducible represen­tations of the whole group. These equations contain an earlier rule as a special case.