Congruence relations characterizing the representation ring of the symmetric group
type: Item
instance of: scholarly article
title: Congruence relations characterizing the representation ring of the symmetric group
zbMATH Open document ID: 0592.20012
DOI: 10.1016/0021-8693(86)90199-7
author: Andreas W. M. Dress
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: It is proven that an arbitrary mapping, \(\chi\), from the partitions of n to \({\mathbb{Z}}\) is a generalized character of the symmetric group on n letters if and only if this mapping satisfies a specified set of congruences. As a corollary, it is demonstrated that \(\chi\) is an irreducible character if and only if \(\chi (1)>0\), \(\sum K(\pi)\chi^ 2(\pi)=n!\), and \(\chi\) satisfies a specified set of congruences.
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 3950803
zbMATH Keywords: generalized character of symmetric group
zbMATH Keywords: partitions
zbMATH Keywords: congruences
zbMATH Keywords: irreducible character
reviewed by: David M. Bressoud
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90199-7
OpenAlex ID: W1967616480
cites work: Transformation groups and representation theory
cites work: Q3952291
cites work: Q4116586
description: scientific article; zbMATH DE number 3950803