Linear Representations of Groups
By: by Ernest B. Vinberg
Series: Basler Lehrbücher, A Series of Advanced Textbooks in Mathematics
Publisher: Birkhäuser Basel
Published: 1989
Place of publication: Basel
Language: eng
ISBN-13: 9783034892742; 9783034899734
Subjects: Algebra; Mathematics
Description: This textbook contains a comprehensive and detailed exposition of the fundamentals of the representation theory of groups, especially of finite groups and compact groups. The exposition is based on the decomposition of the two-sided regular representation. This enables the author to give not only an abstract description of the representations but also their realizations in function spaces, which is important for physical applications. As an example, the theory of Laplace spherical functions is treated. Some basic ideas of the representation theory of Lie groups are also given, as well as all the representations of the groups SU2 and SO3. The book contains numerous examples and exercises, some with solutions.