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.
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References
D. E. Rutherford:Substitutional Analysis (Edinburgh University Press, Edinburgh 1948) pp. 23–44
T. Yamanouchi: Proc. Phys.-Math. Soc. Jpn, 19, 436 (1937)
H. Weyl: The Classical Groups (Princeton University Press, Princeton, 1939) pp. 115–136
G. Racah: Phys. Rev. 76, 1352 (1949)
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© 1990 Springer-Verlag Berlin Heidelberg
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Inui, T., Tanabe, Y., Onodera, Y. (1990). The Symmetric Group. In: Group Theory and Its Applications in Physics. Springer Series in Solid-State Sciences, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80021-4_15
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DOI: https://doi.org/10.1007/978-3-642-80021-4_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60445-7
Online ISBN: 978-3-642-80021-4
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