Symmetry-Adapted Functions Belonging to the Symmetric Groups

Abstract

Young's factorization of idempotents belonging to the symmetric groups is given a necessary and sufficient characterization, by means of a lemma due to Burrow. The use of these idempotents is contrasted with Yamanouchi's representation, and finally the equivalence of Löwdin's path diagram method to the group‐theoretical treatment of the angular momentum states arising from the coupling of an assemblage of spin ½ particles is demonstrated.