Reducible Representations, Irreducible Representations and Characters – Theorems and Properties
S.C. Rakshit · 2021
In this chapter, the authors have to wade through a marshy bog of theorems till the people reach some point from where they can make further explorations. It is the intent of the chapter to probe into the anatomy of the IR’s and the properties of their characters in the form of theorems and their elucidations. Although the full matrices of the different IR’s of a group provide more information on the symmetry properties of a system, the majority of the symmetry problems can be successfully handled with the help of the set of characters of the different IR’s without any need for reference to the explicit forms of the matrices of the IR’s. Conventionally, however, a character table contains more information than just a mere exhibition of the characters of the IR’s. The twin problems of finding basis functions of desired symmetry and the quantitative technique of the reduction of the reducible representation of a group are discussed.