Representation theory of finite and compact groups

Author: Qiu Weisheng
Publisher:
Publish Date: 2001-03-01
Features: This book is based on the author's multiple lectures on the theory of group representations at the Department of Mathematics, Peking University. It elaborates in detail the theory of representations and character theory of finite groups over fields whose characteristic does not divide their order, and also introduces the theory of representations of compact topological groups. The book is divided into six chapters, covering the following content: basic concepts of group representation theory and representations of Abelian groups; representations of finite groups and modules over group algebras; group characters, tensor products of representations, splitting fields, and representations of direct products of groups; induced representations and induced characters; linear representations of compact groups. The book is straightforward in its presentation, progressing from easy to difficult in a systematic and gradual manner. It is well-organized, rigorous in argumentation, detailed in explanations, and emphasizes applications. Each chapter contains numerous examples, and almost every section is accompanied by exercises. Hints are provided for more challenging problems. This book can serve as a textbook for graduate students and senior undergraduate students in mathematics departments, as well as a reference for graduate students in physics and chemistry departments. It can also be used as a reference for mathematicians and scientists engaged in research. Additionally, it is suitable for self-study by readers who have studied linear algebra and abstract algebra.