On the Fourier Expansion of Word Maps
Group Theory
2014-03-26 v1 Representation Theory
Abstract
Frobenius observed that the number of times an element of a finite group is obtained as a commutator is given by a specific combination of the irreducible characters of the group. More generally, for any word w the number of times an element is obtained by substitution in w is a class function. Thus, it has a presentation as a combination of irreducible characters, called its Fourier expansion. In this paper we present formulas regarding the Fourier expansion of words in which some letters appear twice. These formulas give simple proofs for classical results, as well as new ones.
Keywords
Cite
@article{arxiv.1207.0453,
title = {On the Fourier Expansion of Word Maps},
author = {Ori Parzanchevski and Gili Schul},
journal= {arXiv preprint arXiv:1207.0453},
year = {2014}
}