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內容簡介

　　《群的綫性錶示》以作者在莫斯科大學講演稿為藍本，主要目的是盡可能簡明、詳盡地將遇到的問題闡述清楚。書中全麵展示有限群和緊群綫性錶示理論基礎知識，給齣瞭李群綫性錶示理論的基本知識以及李群錶示論的一些基本觀點，詳盡講述瞭群SU2和SO2錶示論部分，作為應用仔細推導瞭拉普拉斯球麵函數。書中有一些例子和練習，並對部分習題附有解答。

內頁插圖

目錄

Preface
Introduction
0 Basic Notions
I General Properties of Representations
1 Invariant Subspaces
2 Complete Reducibility of Representations of Compact Groups
3 Basic Operations on Representations
4 Properties of Irreducible Complex Representations
II Representations of Finite Groups
5 Decomposition Of the Regular Representation
6 Orthogonality Relations
III Representations of Compact Groups
7 The Groups SU2 and SO3
8 Matrix Elements of Compact Groups
9 The Laplace Spherical Functions
IV Representations of Lie Groups
10 General Properties of Homomorphisms and Representations of Lie Groups
11 Representations of SU2 and SO3
Appendices
A1 Presentation of Groups By Means of Generators and Relations
A2 Tensor Products
A3 The Convex Hull of a Compact Set
A4 Conjugate Elements in Groups
Answers and Hints to Exercises
List of Notations
References
Index

前言/序言

　　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].

群的綫性錶示 [Linear Representations of Croups] 下載 mobi epub pdf txt 電子書

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