Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer

Front Matter
	Cover
	Title page
	Dedication
	Contents
	Preface
	Photo Credits
	Archival Sources
Chapter I. Some 19th-century Algebra and Number Theory
	1. Introduction
	2. Ruler and Compass Constructions and Cyclotomic Fields
	3. Equations Defining Subfields of the Cyclotomic Field
	4. The Quadratic Subfield of the Cyclotomic Field
	5. Lagrange Resolvents and Gauss Sums
	6. Quadratic Reciprocity: a proof based on Gauss sums
	7. Dirichlet's L-series and Characters mod k
	8. Characters associated with quadratic forms
Chapter II. Frobenius and the Invention of Character Theory
	1. Frobenius in Berlin and Zürich: 1850-1900
	2. Research on Finite Groups and Number Theory: 1880-1896
	3. Characters of Finite Groups
	4. Group Representations and Characters
	5. The Characters of the Symmetric Group
	6. An Application of Character Theory: Frobenius Groups
Chapter III. Burnside: Representations and Structure of Finite Groups
	1. Burnside at Cambridge and Greenwich
	2. Burnside's Early Research on Finite Groups: 1890-1900
	3. From Lie Groups to Representations of Finite Groups: 1898-1900
	4. Foundations of Representation Theory: 1900-1905
	5. The p^a q^b -Theorem and Other Applications of Character Theory
Chapter IV. Schur: A New Beginning
	1. Issai Schur in Berlin: 1894-1939
	2. Schur's New Foundations of Character Theory
	3. Joint Work of Frobenius and Schur: 1905-1906
	4. The Schur Index
	5. Projective Representations of Finite Groups
	6. Permutation Groups and Centralizer Rings
Chapter V. Polynomial Representations of GL_n(C)
	1. Invariant Theory and Representations of GL_n: Jacques Deruyts
	2. Polynomial Representations of GL_n: Issai Schur
	3. Schur's Character Formula
Chapter VI. Richard Brauer and Emmy Noether: 1926-1933
	1. Richard Brauer in Berlin, Königsberg, and North America
	2. Emmy Noether and her Impact on Representation Theory
	3. Simple Algebras and the Brauer Group: 1926-1933
Chapter VII. Modular Representation Theory
	1. Brauer and Nesbitt: Opening Moves
	2. Nonsemisimple Algebras: Brauer, Nakayama, and Nesbitt
	3. Blocks and the Classification of Finite Simple Groups
	4. The Brauer Induction Theorem and its Applications
Bibliography
Index
Errata
Back Cover