The Symmetric Group
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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 Representation Symmetric Group Unitary Group Young Diagram Irreducible Character
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- 15.3H. Weyl: The Classical Groups (Princeton University Press, Princeton, 1939) pp. 115–136Google Scholar