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Titlebook: Linear Representations of Groups; Translated from the Ernest B. Vinberg Book 1989 Birkhäuser Verlag 1989 Laplace spherical functions.Repre

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书目名称Linear Representations of Groups
副标题Translated from the
编辑Ernest B. Vinberg
视频video
概述Brief, modern and very readable introduction to representation theory of groups.Clear and concentrating on the essentials.Provides numerous examples and exercises, some with solutions.Includes supplem
丛书名称Modern Birkhäuser Classics
图书封面Titlebook: Linear Representations of Groups; Translated from the  Ernest B. Vinberg Book 1989 Birkhäuser Verlag 1989 Laplace spherical functions.Repre
描述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 r
出版日期Book 1989
关键词Laplace spherical functions; Representation theory; compact groups; finite groups; homomorphism; represen
版次1
doihttps://doi.org/10.1007/978-3-0348-0063-1
isbn_softcover978-3-0348-0062-4
isbn_ebook978-3-0348-0063-1Series ISSN 2197-1803 Series E-ISSN 2197-1811
issn_series 2197-1803
copyrightBirkhäuser Verlag 1989
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Modern Birkhäuser Classicshttp://image.papertrans.cn/l/image/586413.jpg
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978-3-0348-0062-4Birkhäuser Verlag 1989
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Linear Representations of Groups978-3-0348-0063-1Series ISSN 2197-1803 Series E-ISSN 2197-1811
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Representations of Finite Groups,In this chapter we are concerned only with finite-dimensional representations, mainly complex ones. Recall that in Section 2 we have shown that every complex linear representation of a finite group is unitary, and hence completely reducible.
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Representations of Compact Groups,pact topological groups are in many respects similar to finite groups. In this chapter we examine the simplest examples of connected compact groups and their linear representations, and we generalize to compact linear groups the main theorems on matrix elements proven in the preceding chapter for finite groups.
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