Representations of finite and compact groups / Barry Simon

Auteur principal : Simon, Barry, 1946-, AuteurType de document : MonographieCollection : Graduate studies in mathematics, 10Langue : anglais.Pays: Etats Unis.Éditeur : Providence : American Mathematical Society, 1996Description : 1 vol. (XII-266 p.) : ill. ; 26 cmISBN: 0821804537.ISSN: 1065-7339.Bibliographie : Bibliogr. p. 261. Index.Sujet MSC : 22E15, Lie groups, General properties and structure of real Lie groups
20C30, Group theory - Representation theory of groups, Representations of finite symmetric groups
22E46, Lie groups, Semisimple Lie groups and their representations
20C15, Group theory - Representation theory of groups, Ordinary representations and characters
En-ligne : Zentralblatt | MathSciNet | AMS
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Bibliogr. p. 261. Index

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. (Zentralblatt)

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