Commuting-Operator Approach to Group Representation Theory

Abstract

A study is given of the class‐sum‐operator approach to the representation theory of finite groups, the group D 3h being specifically studied. The class sum approach is shown to simplify the decomposition of Kronecker products. By using the class‐sum‐operator approach, it is shown that the ``indirect'' group‐projection operators of Löwdin can be used in finite group theory, where they lead to useful factorizations of the finite group‐projection operators. It is also shown that tensor operators of certain symmetry types can be constructed within the group itself, and may be used analogously to the usual operator equivalents of crystal field theory.