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.
Table of Contents
Groups and Subgroups
Point Groups and Cosets
Homomorphisms and Normal Subgroups
Isomorphisms and Automorphisms
Representations of Abelian Groups
Orthogonality Relations and Character Tables
The Burnside Counting Theorem
Induced Representations and Characters
The Character Table for S5
Space Groups and Semi-Direct Products
Proofs of the Sylow Theorems
Index of Symbols.
"…rigorous and appropriate…excellent starting point for anyone interested in the theory of groups, representations and characters. Upper division undergraduates through professionals."
-D. S. Larson, Gonzago University in CHOICE