Linear Representations of Groups - Couverture rigide

Couverture rigide

ISBN 10 : 3764322888 ISBN 13 : 9783764322885

Editeur : Birkhauser Verlag AG, 1989

Synopsis

This book gives an exposition of the fundamentals of the theory of linear representations of finite and compact groups, as well as elements of the the- ory of linear representations of Lie groups. As an application we derive the Laplace spherical functions. The book is based on lectures that I delivered in the framework of the experimental program at the Mathematics-Mechanics Faculty of Moscow State University and at the Faculty of Professional Skill Improvement. My aim has been to give as simple and detailed an account as possible of the problems considered. The book therefore makes no claim to completeness. Also, it can in no way give a representative picture of the modern state of the field under study as does, for example, the monograph of A. A. Kirillov [3]. For a more complete acquaintance with the theory of representations of finite groups we recommend the book of C. W. Curtis and I. Reiner [2], and for the theory of representations of Lie groups, that of M. A. Naimark [6]. Introduction The theory of linear representations of groups is one of the most widely ap- plied branches of algebra. Practically every time that groups are encountered, their linear representations play an important role. In the theory of groups itself, linear representations are an irreplaceable source of examples and a tool for investigating groups. In the introduction we discuss some examples and en route we introduce a number of notions of representation theory. O.

A propos du livre

Présentation de l'éditeur

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.

Biographie de l'auteur

Ernest B. Vinberg is a Professor of mathematics at the Moscow University.

Détails de l'édition

• Éditeur: Birkhauser Verlag AG
• Date d'édition: 1989
• Langue: anglais
• ISBN 10: 3764322888
• ISBN 13: 9783764322885
• Reliure: Relié
• Nombre de pages: 146
• Éditeur: Vinberg Ernest Borisovich
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible