The year 1897 was marked by two important mathematical
events: the publication of the first paper on representations of
finite groups by Ferdinand Georg Frobenius (1849–1917) and the
appearance of the first treatise in English on the theory of finite
groups by William Burnside (1852–1927). Burnside soon developed
his own approach to representations of finite groups. In the next few
years, working independently, Frobenius and Burnside explored the new
subject and its applications to finite group theory.
They were soon joined in this enterprise by Issai Schur
(1875–1941) and some years later, by Richard Brauer
(1901–1977). These mathematicians' pioneering research is the
subject of this book. It presents an account of the early history of
representation theory through an analysis of the published work of the
principals and others with whom the principals' work was
interwoven. Also included are biographical sketches and enough
mathematics to enable readers to follow the development of the
subject. An introductory chapter contains some of the results
involving characters of finite abelian groups by Lagrange, Gauss, and
Dirichlet, which were part of the mathematical tradition from which
Frobenius drew his inspiration.
This book presents the early history of an active branch of
mathematics. It includes enough detail to enable readers to learn the
mathematics along with the history. The volume would be a suitable
text for a course on representations of finite groups, particularly
one emphasizing an historical point of view.
Readership
Graduate students and research mathematicians; mathematical
historians.
