Linear Representations of Groups

Translated from the Russian by A. Iacob
1. Auflage 1989. 2. printing 2010
ISBN: 978-3-0348-0062-4
Verlag: Springer

Buch, Englisch, 146 Seiten, Book, Format (B × H): 158 mm x 241 mm, Gewicht: 244 g

Reihe: Progress in Nonlinear Differential Equations and Their Applications

This book gives an exposition of the fundamentals of the theory of linear representations of ?nite and compact groups, as well as elements of the t- 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 ?eld under study as does, for example, the monograph of A. A. Kirillov [3]. For a more complete acquaintance with the theory of representations of ?nite 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 - pliedbranchesof algebra. Practically every timethatgroupsareencountered, 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. 0. Basic Notions 0. 1.

Zielgruppe

Research

Autoren/Hrsg.

Vinberg, Ernest B.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

General Properties of Representations.- Representations of Finite Groups.- Representations of Compact Groups.- Representations of Lie Groups.- Appendices.

Über Autor(innen)

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