The symmetric group: Characters, products and plethysms

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.