The Symmetric Group

Abstract

In this chapter, fundamentals of the symmetric group, namely, classes of permutations, Young diagrams, irreducible characters, and the construction of irreducible representations and their bases, are reviewed and summarized.The relation between the irreducible representations of the symmetric group and tensor representations of the unitary group is essential in understanding the wavefunctions of a many-electron atom with a definite magnitude of spin S. We have also seen that the concepts of symmetric and antisymmetric product representations play important roles in other fields covered in this book.KeywordsIrreducible RepresentationSymmetric GroupUnitary GroupYoung DiagramIrreducible CharacterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.