On the Fourier expansion of word maps. (24th September 2013)

• Record Type: Journal Article
• Authors: Parzanchevski, Ori; Schul, Gili
• Is Part Of: Bulletin of the London Mathematical Society. Volume 46:Part 1(2014:Feb.)
• Page Start: 91
• Page End: 102
• Publication Date: 2013-09-24
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/blms/bdt068
• Languages: English
• ISSNs: 0024-6093

Abstract

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 the Fourier expansion of w . 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.