ABSTRACT

Group representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. This book offers an easy-to-follow introduction to the theory of groups and of group characters. Designed as a rapid survey of the subject, it emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. The text includes sections that provide the mathematical basis for some of the applications of group theory. It also offers numerous exercises, some stressing computation of concrete examples, others stressing development of the theory.

chapter 1|9 pages

Introductory Examples

chapter 2|9 pages

Groups and Subgroups

chapter 3|12 pages

Point Groups and Cosets

chapter 4|10 pages

Homomorphisms and Normal Subgroups

chapter 5|8 pages

Isomorphisms and Automorphisms

chapter 6|8 pages

Factor Groups

chapter 7|10 pages

Sylow Subgroups

chapter 8|10 pages

Permutation Groups

chapter 9|6 pages

Matrix Groups

chapter 10|12 pages

Group Representations

chapter 11|8 pages

Regular Representations

chapter 12|14 pages

Irreducible Representations

chapter 13|12 pages

Representations of Abelian Groups

chapter 14|12 pages

Group Characters

chapter 15|12 pages

Orthogonality Relations and Character Tables

chapter 16|10 pages

Reducible Characters

chapter 17|8 pages

The Burnside Counting Theorem

chapter 18|12 pages

Real Characters

chapter 19|14 pages

Induced Characters

chapter 20|8 pages

The Character table for S5

chapter 21|18 pages

Space Groups and Semidirect Products

chapter 22|6 pages

Proofs of the Sylow Theorems