Total characters and Chebyshev polynomials.
type: Item
instance of: scholarly article
title: Total characters and Chebyshev polynomials.
zbMATH Open document ID: 1034.20012
DOI: 10.1155/S0161171203201046
author: Eirini Poimenidou
author: Homer Wolfe
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-12-03T00:00:00Z
full work available at URL: https://eudml.org/doc/50672
review text: Summary: The total character \(\tau\) of a finite group \(G\) is defined as the sum of all the irreducible characters of \(G\). K. W. Johnson asked when it is possible to express \(\tau\) as a polynomial with integer coefficients in a single irreducible character. In this paper, we give a complete answer to Johnson's question for all finite dihedral groups. In particular, we show that, when such a polynomial exists, it is unique and it is the sum of certain Chebyshev polynomials of the first kind in any faithful irreducible character of the dihedral group \(G\).
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 33C80
zbMATH DE Number: 2012549
zbMATH Keywords: total characters
zbMATH Keywords: finite dihedral groups
zbMATH Keywords: irreducible characters
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: Gelfand models
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2012549