群的線性表示

前言

　　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].

內(nèi)容概要

本書以作者在莫斯科大學(xué)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。書中全面展示有限群和緊群線性表示理論基礎(chǔ)知識，給出了李群線性表示理論的基本知識以及李群表示論的一些基本觀點，詳盡講述了群SU2和SO2表示論部分，作為應(yīng)用仔細推導(dǎo)了拉普拉斯球面函數(shù)。書中有一些例子和練習(xí)，并對部分習(xí)題附有解答。

書籍目錄

PrefaceIntroduction  0 Basic NotionsI 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 RepresentationsII Representations of Finite Groups  5 Decomposition Of the Regular Representation  6 Orthogonality RelationsIII Representations of Compact Groups  7 The Groups SU2 and SO3  8 Matrix Elements of Compact Groups  9 The Laplace Spherical FunctionsIV Representations of Lie Groups  10 General Properties of Homomorphisms and Representations of Lie Groups  11 Representations of SU2 and SO3Appendices  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 GroupsAnswers and Hints to ExercisesList of NotationsReferencesIndex

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