有限群的线性表示
2008-10
世界图书出版公司
Jean-Pierre Serre
170
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This book consists of three parts, rather different in level and purpose:The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. This is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics. I have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra.The examples (Chapter 5) have been chosen from those useful to chemists.
本书是一部非常经典的介绍有限群线性表示的教程，原版曾多次修订重印，作者是当今法国最突出的数学家之一，他对理论数学有全面的了解，尤以著述清晰、明了闻名。本书是他写的为数不多的教科书之一，原文是法文（1971年版），后出了德译本和英译本。本书是英译本的重印本。它篇幅不大，但深入浅出的介绍了有限群的线性表示，并给出了在量子化学等方面的应用，便于广大数学、物理、化学工作者初学时阅读和参考。
作者：(法国)赛尔 (Serre.J.P)
Part ⅠRepresentations and Characters 1 Generalities on linear representations 1.1 Definitions 1.2 Basic examples 1.3 Subrepresentations 1.4 Irreducible representations 1.5 Tensor product of two representations 1.6 Symmetiic square and alternating square 2 Character theory 2.1 The character of a representation 2.2 Schur's lemma; basic applications 2.3 Orthogonality'reiations for characters 2.4 Decomposition of the regular representation 2.5 Number of irreducible representations 2.6 Canonical decomposition of a representation 2.7 Explicit decomposition of a representation 3 Subgroups, products, induced representations 3.1 Abelian subgroups 3.2 Product of two groups 3.3 Induced representations 4 Compact groups 4.1 Compact groups 4.2 lnvariant measure on a compact group 4.3 Linear representations of compact groups 5 Examples 5.1 The cyclic Group Cn 5.2 The group C 5.3 The dihedral group D 5.4 The group Dn 5.5 The group D 5.6 The group D 5.7 The alternating group 5.8 The symmetric group 5.9 The group of the cube Bibliography: Part IPart Ⅱ Representations in Characteristic Zero 6 The group algebra 6,1 Representations and modules 6.2 Decomposition of C[G] 6.3 The center of C[G] 6.4 Basic properties of integers 6.5 lntegrality properties of characters. Applications 7 Induced representations; Mackey's criterion 7.1 Induction 7.2 The character of an induced representation; the reciprocity formula 7.3 Restriction to subgroups 7.4 Mackey's irreducibility criterion 8 Examples of induced representations 8.1 Normal subgroups; applications to the degrees of the irreducible representations 8.2 Semidirect products by an abelian group 8.3 A review of some classes of finite groups 8.4 Sylow's theorem 8.5 Linear representations of supersolvable groups 9 Artin's theorem 9.1 The ring R(G) 9,2 Statement of Artin's theorem 9.3 First proof 9.4 Second proof of (i) (ii) 10 A theorem of Brauer 10.1 p-regular elements;p-elementary subgroups 10.2 Induced characters arising from p-elementary subgroups 10.3 Construction of characters 10.4 Proof of theorems 18 and 18' 10,5 Brauer's theorem ……part Ⅲ Introduction to Brauer TheoryAppendixBibliography:Part ⅢIndex of notationIndex of terminology
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《有限群的线性表示》由世界图书出版公司出版。
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有限群表示论最经典的书。
有一点群论的基础都可以读的，很基础
Serre的经典之作
GTM丛书之一，值得收藏、研读。。。
J.P.Serre的书，值得信赖
书很好，就是字感觉有点小，质量不错
经典教材,不错的书.
这本群表示论的书写得非常精彩。Serre的书一直以简洁明了著称，这就是其中的典型。Serre从最简单的复数域上的有限维表示讲起，一直讲到了Grothendieck的一些理论。
serre的水平毋庸置疑，据说他研究问题的思路如泉水一般清晰，值得拜读一下。