Squares of characters in \(A_ n\) with a small number of irreducible constituents
type: Item
instance of: scholarly article
title: Squares of characters in \(A_ n\) with a small number of irreducible constituents
zbMATH Open document ID: 0776.20004
author: Ilan Zisser
published in: Journal of Algebra
publication date: 1993-03-29T00:00:00Z
review text: The main result of the present paper (which corresponds to a part of the author's Ph.D. thesis) is the following Theorem: Let \(\chi\) be a non- principal irreducible character of \(A_ n\), \(n\geq 5\). Then the number \(S(\chi)\) of irreducible constituents of \(\chi^ 2\) is \(\geq 5\) unless one of the following occurs: --- \(n=5\) and \(\chi\) is a son of \(\zeta^{(3,1^ 2)}\). In this case \(S(\chi)=3\). --- \(n=6\) and \(\chi\) is a son of \(\zeta^{(3^ 2)}\). In this case \(S(\chi)=4\). --- \(n\geq 6\) and \(\chi\) is a son of \(\zeta^{(n-1,1)}\). In this case \(S(\chi)=4\). (A son is an irreducible constituent of a restriction of an irreducible character of the symmetric group to the alternating group.) The proof uses classical results on inner tensor products, and new results of the author, some of which appeared in a recent paper [in J. Algebra 153, 357- 372 (1992)]).
reviewed by: Adalbert Kerber
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 130513
zbMATH Keywords: number of irreducible constituents
zbMATH Keywords: irreducible character
zbMATH Keywords: alternating group
zbMATH Keywords: inner tensor products
MaRDI profile type: Publication
full work available at URL: jabr.1993.1012
OpenAlex ID: W2056957623
DOI: 10.1006/JABR.1993.1012
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description: scientific article; zbMATH DE number 130513