半单群的表示论.第1卷(英文版)
基本信息
- 原书名:Representation Theory of Semisimple Groups: An Overview Based on Examples
- 原出版社: Princeton University Press
- 作者: Anthony W. Knapp
- 出版社:世界图书出版公司
- ISBN:9787510029585
- 上架时间:2011-1-27
- 出版日期:2011 年1月
- 开本:24开
- 页码:384
- 版次:1-1
- 所属分类:
数学 > 代数,数论及组合理论 > 群表示论
编辑推荐
半单群的经典著作
定理陈述详细
内容覆盖全面
推荐阅读
内容简介回到顶部↑
本书是一部经典的著作,分为上下两卷,前十章为上卷,后六章为下卷。书中讲述半单李群表示理论的方式给出了本科目的精华,符合学习的自然规律。定理陈述地相当详细,增加了许多经典的解释性例子。本章末都有习题,对于学习研究生和科研工作者相当有用。目次:理论概述;su(2),su(2,r)和su(2,c)表示论;c∞向量和通用包络代数;紧李群表示论;非紧群的理论;全纯离散系列;导出表示论;可允许表示论;离散系列的结构;全局性质;plancherel公式;不可约表示论;最小k型;酉表示;附录:李群的基本理论;偏微分方程的常规奇异点;经典群的根和受限根。
读者对象:数学专业的研究生和相关的科研人员。
读者对象:数学专业的研究生和相关的科研人员。
目录回到顶部↑
preface to the princeton landmarks in mathematics edition
preface
acknowledgments
chapter i. scope of the theory
1.the classical groups
2.cartan decomposition
3.representations
4.concrete problems in representation theory
5. abstract theory for compact groups
6.application of the abstract theory to lie groups
7.problems
chapter ii. representations of su(2), sl(2, r), and sl(2, c)
1.the unitary trick
2.irreducible finite-dimensional complex-linear representations of si(2, c)
3.finite-dimensional representations of s1(2, c)
4.irreducible unitary representations of sl(2, c)
5.irreducible unitary representations of sl(2, r)
6.use of su(1, 1)
7.plancherel formula
8.problems
preface
acknowledgments
chapter i. scope of the theory
1.the classical groups
2.cartan decomposition
3.representations
4.concrete problems in representation theory
5. abstract theory for compact groups
6.application of the abstract theory to lie groups
7.problems
chapter ii. representations of su(2), sl(2, r), and sl(2, c)
1.the unitary trick
2.irreducible finite-dimensional complex-linear representations of si(2, c)
3.finite-dimensional representations of s1(2, c)
4.irreducible unitary representations of sl(2, c)
5.irreducible unitary representations of sl(2, r)
6.use of su(1, 1)
7.plancherel formula
8.problems
前言回到顶部↑
I am pleased that Princeton University Press has decided to reprint in its Landmarks in Mathematics series Representation Theory of Semisimple Groups: An Overview Based on Examples. The original hardback edition of the book has been out of print for two years, and the book continues to be in demand.
The subject matter is at least as important today as it was at the time of the book's original publication in 1986. Two of the fields of application--automorphic forms and analysis of semisimple symmetric spaces--have un-dergone remarkable advances, and the theory in the book has been indis-pensable for both. Newer fields, such as Kac-Moody algebras and quantum groups, show promise of using more and more of this theory. And attempts at solving the key problem in Chapter XVI--that of finding all the irreduc-ible unitary representations for all semisimple groups--have led to new ap-proaches and new problems in the subjects of algebraic groups and geomet-ric group actions.
Even with all these advances, the approach taken in the hardback edition continues to be an appropriate one for learning the subject. None of the text has been changed in the Landmarks edition, and thus it remains true to this approach.
A.W.K.
April 2001
The subject matter is at least as important today as it was at the time of the book's original publication in 1986. Two of the fields of application--automorphic forms and analysis of semisimple symmetric spaces--have un-dergone remarkable advances, and the theory in the book has been indis-pensable for both. Newer fields, such as Kac-Moody algebras and quantum groups, show promise of using more and more of this theory. And attempts at solving the key problem in Chapter XVI--that of finding all the irreduc-ible unitary representations for all semisimple groups--have led to new ap-proaches and new problems in the subjects of algebraic groups and geomet-ric group actions.
Even with all these advances, the approach taken in the hardback edition continues to be an appropriate one for learning the subject. None of the text has been changed in the Landmarks edition, and thus it remains true to this approach.
A.W.K.
April 2001

点击看大图




加载中...