The symmetric group: Characters, products and plethysms
- 1 September 1973
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 14 (9), 1176-1183
- https://doi.org/10.1063/1.1666459
Abstract
It is demonstrated following the work of Murnaghan and Littlewood that the symmetric group may with advantage be considered as a subgroup, albeit finite, of the general linear group. This approach involves in a natural way the use of a reduced notation for the specification of irreducible representations of Σ n and leads to the determination of closed formulas for the dimension, characters, and Kronecker products of such representations. The relationship between the characters and S functions is discussed in detail and some results on symmetrized Kronecker squares are obtained.Keywords
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