Q1121377
type: Item
instance of: scholarly article
title: 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)
zbMATH Open document ID: 0674.20005
DOI: 10.1007/BF01188668
author: Thomas Scharf
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20B30
zbMATH DE Number: 4103328
zbMATH Keywords: symmetric group
zbMATH Keywords: permutation representation
zbMATH Keywords: irreducible representation
zbMATH Keywords: character table
zbMATH Keywords: conjugating representation
MaRDI profile type: Publication
cites work: Theorem about the conjugacy representation of \(S_ n\)
cites work: Q3952291
full work available at URL: https://doi.org/10.1007/bf01188668
OpenAlex ID: W2008254529
label: 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)
description: scientific article; zbMATH DE number 4103328