Abstract
Up to now we have studied the unitary groups SU(N), especially those with N = 2, 3, 4 and 6 dimensions. Now we want to discuss some properties of the permutation group SN, which is also called the symmetric group. The group S N is important if we have to deal with several identical particles. In this section we will aquaint ourselves with the concept of Young diagrams, which in turn is useful for the construction of the basis functions of the unitary irreducible representations of SU(N).
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References
In the literature one sometimes distinguishes between Young diagrams and Young tableaux: the nomenclature says that a tableau is a diagram containing a positive number in each box.
See, e.g., W.K. Tung: Group Theory in Physics (World Scientific, Singapore 1985), Chap. 5.
A proof of this theorem is found in B.G. Wyborne: Classical Groups for Physicists (Wiley, New York 1974), Chap. 22.
H.J. Coleman: Symmetry Groups made easy, Adv. Quantum Chemistry 4, 83 (1968).
D.B. Lichtenberg: Unitary symmetry and elementary particles (Academic Press, New York, London 1970) Chap. 7.4.
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© 1994 Springer-Verlag Berlin Heidelberg
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Greiner, W., Müller, B. (1994). Representations of the Permutation Group and Young Tableaux. In: Quantum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57976-9_9
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DOI: https://doi.org/10.1007/978-3-642-57976-9_9
Publisher Name: Springer, Berlin, Heidelberg
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