Group representation theory

Author: Cao Xihua / Ye Jiaschen (editors)
Publisher:
Publish Date: 2000-04-01
Features: Representation theory is a rapidly developing and highly active branch of modern mathematics. It has extensive applications in research fields such as quantum mechanics, quantum chemistry, nuclear structure, solid-state physics, field theory, and more. This book aims to comprehensively present the theory of group representations. The book is divided into four chapters, covering the following content:
Finite group representations, including the basic concepts of linear representations, character theory, and a series of important results on induced representations;
Finite group modular representations, including Brauer character theory, the fundamental properties of Cartan-Brauer triangles, and the theory of blocks;
Representation theory of topological groups, including representations of compact topological groups and characteristic theory, the Peter-Weyl theorem, and the duality theory of locally compact abelian groups, etc.
To facilitate readers, the book strives to be self-contained. In each chapter, the fundamentals of group theory, modules, and algebra are systematically introduced. In the appendix, the content of topological spaces, projective limits, and Zorn's lemma is briefly presented.
After each section, there are an adequate number of exercises to help readers understand and expand upon the main content. Readers with a solid foundation in linear algebra can use this book. It can serve as a textbook for graduate students and senior undergraduate students in mathematics and physics departments to study finite group representation theory or topological group representation theory. It is also suitable for scientific workers and university teachers in related fields.