Representations of finite and compact groups. (English) Zbl 0840.22001

Simon, Barry

Graduate Studies in Mathematics. 10. Providence, RI: American Mathematical Society (AMS). xii, 266 p. (1996).

This book contains a very good explanation of representation theory of finite and compact groups and can be recommended to everyone for learning or teaching representation theory. There are two parts (Chapters I–VI and VII–IX) corresponding to the cases of finite resp. compact groups, where by “compact groups” compact Lie groups are meant. The presentation is relatively elementary, very clear and systematic. The foundations and the general theory are presented as well as an outline of the representation theory of well known important groups.
The chapters are: I. Groups and Counting Principles, II. Fundamentals of Group Representations, III. Abstract Theory of Representations of Finite Groups, IV. Representations of Concrete Finite Groups. I: Abelian and Clifford Groups, V. Representations of Concrete Finite Groups. II: Semidirect Products and Induced Representations, VI. Representations of Concrete Finite Groups. III: The Symmetric Groups, VII. Compact Groups, VIII. The Structure of Compact Semisimple Groups, IX. The Representations of Compact Semisimple Groups.

Reviewer: G.Czichowski (Greifswald)

MSC:

22-02	Research exposition (monographs, survey articles) pertaining to topological groups
22E46	Semisimple Lie groups and their representations
20C15	Ordinary representations and characters
20C30	Representations of finite symmetric groups
22E15	General properties and structure of real Lie groups
20-02	Research exposition (monographs, survey articles) pertaining to group theory

Keywords:

compact groups; finite groups; Clifford groups; symmetric groups; semisimple groups; representation; Lie groups