Ein weiterer Beweis, daß die konjugierende Darstellung der symmetrischen Gruppe jede irreduzible Darstellung enthält. (A further proof that the conjugating representation of the symmetric group contains every irreducible representation)
In this note we give a different proof of the following result of \textit{A. Frumkin} [Isr. J. Math. 55, 121-128 (1986; Zbl 0606.20019)]: Consider the symmetric group in n letters (n\(\neq 2)\) acting on itself by conjugation: \((\pi,\sigma)\mapsto \pi \sigma \pi^{-1}\). Then the corresponding permutation representation over a field of characteristic zero contains each irreducible representation at least once, or, equivalently, the row sums of the character table are strictly positive. The method used is to show that this conjugating representation contains the model as it is given by \textit{N. Inglis} and \textit{J. Saxl} [Arch. Math. (to appear)].
scientific article; zbMATH DE number 4103328