New light on Frobenius' creation of the theory of group characters

Abstract

In an earlier paper [1971] I sketched the background to Frobenius' creation of the theory of group characters and sought to determine the role played therein by Richard Dedekind. An important source f insight was provided by Dedekind's letters to Frobenius, portio s of which were publi hed in Dedekind's Werke [1931 : 414-442]. Unfortunately, my efforts to locate Frobenius' part of th correspondence were unsuccessful, and it seemed t be ir etrievably lost. Recently, h wever, it was expectedly discover d by Kim rling [1972 : § 8] and is now located in the Clifford Memorial Library, University of Evansville, Indiana.1 The purpose of this paper is to co plete the historical anal sis of the origins of the t ory of group characters begun in my paper [1971]. There the empha is was necessarily upon Dedekind and the u ber-theoretic tradition which motivated his work. The Evansville ma uscripts now mak it possible o portray Fr benius1 role in much greater detail. The correspondence between Dedekind and Frobenius runs to more than 300 pages and falls in the periods I882-83, 1895-98, I90I. Frobenius' share amounts to 1 78 pages, many of them written in April of 1 8 6 when he was creating the theory of group ch racters as we now k ow iti.e. as opposed to the rlier, li i ed form of the theory developed by Dedekind for Abelian groups. These pages are virtually reports on " ork in progress" to Dedekind and provide invaluabl insight into the manner in which Frob nius was led to his gene alized characters and their funda e tal properties (Sections 3 and 4). It turns out that