Abstract
The symmetric (permutation) group is an important prototype of finite groups. In fact, Cayley’s theorem (see Rotman in An Introduction to the Theory of Groups, Allyn and Bacon, Needham Heights, [Rotm 84, p. 46] for a proof) states that any finite group of order n is isomorphic to a subgroup of S n . Moreover, the representation of S n leads directly to the representation of many of the Lie groups encountered in physical applications. It is, therefore worthwhile to devote some time to the analysis of the representations of S n .
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Notes
- 1.
We must make the additional assumption that the permuted functions are all independent.
References
Boerner, H.: Representation of Groups. North-Holland, Amsterdam (1963)
Hamermesh, M.: Group Theory and Its Application to Physical Problems. Dover, New York (1989)
Rotman, J.: An Introduction to the Theory of Groups, 3rd edn. Allyn and Bacon, Needham Heights (1984)
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Hassani, S. (2013). Representations of the Symmetric Group. In: Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-01195-0_25
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DOI: https://doi.org/10.1007/978-3-319-01195-0_25
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