Olejar Books

The theory of group representations is an elegant subject at the intersection of algebra, geometry, and analysis, with applications to crystallography, chemistry, and the physics of atomic and subatomic particles. This book is an introduction to both the theory and applications of group representations. The author lends coherence to this vast subject by focusing on the connections between group representations and the study of symmetry. The book begins with a brisk review of the basic definitions and fundamental results of group theory. Definitions are illustrated with examples important to the study of symmetry, such as the symmetric group and the Lie groups SU(2) and SO(3). The representation theory of finite groups is introduced in Chapter 2, and the principle results generalized to compact groups in Chapter 3. In later chapters Lie groups are introduced, with the Lie groups SU(2) and SO(3) and their representations studied in detail. Chapter 7 on spherical harmonics connects SO(3) to applications in electrodynamics and quantum mechanics, while Chapter 8 applies SU(2) to the study of quarks. With only linear algebra and calculus as prerequisites, this book will be accessible to both advanced undergraduates and beginning graduate students. An extensive collection of exercises, many with answers or complete solutions, makes this an ideal text for the classroom or independent study.