Items related to Linear Representations of Groups: 2 (Basler Lehrbucher)
Synopsis
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.
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Review
From the reviews:
“Vinberg’s book should be seen as preliminary to far more ambitious and weighty texts ... . It takes the reader from raw basics, done very nicely, through the obligatory discussion of the regular representation ... to some excellent stuff on SU2 and SO3, with a discussion of Laplace’s spherical functions thrown in. The presence of a huge number of guiding examples is a major asset ... as is the large collection of exercises for the reader. It is indeed a marvelous introduction to representation theory!” (Michael Berg, The Mathematical Association of America, February, 2011)
About the Author
Ernest B. Vinberg is a Professor of mathematics at the Moscow University.
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Linear Representations of Groups. Translated from the Russian by A. Iacob.Basler Lehrbucher: A Series of Advanced Textbooks in Mathematics, Vol. 2
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