Representations

Having made acquaintance with the basic properties of groups, we now turn our attention to the structure of the matrices which represent the group action in a function spaceFunction space. It turns out that there exists only a limited set of standard patterns. These are called the irreducible representationsRepresentationirreducible. They form the principal mathematical concept on which this monograph is based, and much care is devoted to acquire a gradual understanding of what this concept really means. Then the character theoremCharactertheorem, matrix theorems, and projection operatorsOperatorprojection are introduced. The concepts of subductionSubduction and inductionInduction relate the representations of subgroupsSubgroup and those of their parent group. The chapter also offers a detailed group-theoretical analysis of three chemical applications: the tetrahedral hybridization of carbon, the molecular vibrations of \(\text {PF}_5\) and \(\text {UF}_6\) , and the electronic structure and magnetic properties of conjugated hydrocarbonsHydrocarbon, according to the Hückel and LondonMagnetiLondon models.