The symmetric group: Characters, products and plethysms
Philip H. Butler, Ronald C. King · Journal of Mathematical Physics · 1973
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 Σn 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.