紧李群的表示

所属分类:数学  
出版时间:1999-11   出版时间:世界图书出版公司   作者:Theodor Brocker,Tammo Tom Dieck   页数:313  
Tag标签:GTM,数学,Springer,表示论  

内容概要

This book is based on several courses given by the authors since 1966. It introduces the reader to the representation theory of compact Lie groups. We have chosen a geometrical and analytical approach since we feel that this is the easiest way to motivate and establish the theory and to indicate relations to other branches of mathematics. Lie algebras, though mentioned occasionally, are not used in an essential way. The material as well as its presentation are classical; one might say that the foundations were known to Hermann Weyl at least 50 years ago.

书籍目录

CHAPTER

Lie
Groups
and
Lie
Algebras
1.
The
Concept
of
a
Lie
Group
and
the
Classical
Examples
2.
Left-Invariant
Vector
Fields
and
One-Parameter
Groups
3.
The
Exponential
Map
4.
Homogeneous
Spaces
and
Quotient
Groups
5.
Invariant
Integration
6.
Clifford
Algebras
and
Spinor
Groups
CHAPTER

Elementary
Representation
Theory
1.
Representations
2.
Semisimple
Modules
3.
Linear
Algebra
and
Representations
4.
Characters
and
Orthogonality
Relations
5.
Representations
of
SU(2),
SO(3),
U(2),
and
O(3).
6.
Real
and
Quaternionic
Representations
7.
The
Character
Ring
and
the
Representation
Ring
8.
Representations
of
Abelian
Groups
9.
Representations
of
Lie
Algebras
10.
The
Lie
Algebra
sl(2,
C)
CHAPTER

Representative
Functions
1.
Algebras
of
Representative
Functions
2.
Some
Analysis
on
Compact
Groups
3.
The
Theorem
of
Peter
and
Wey1
4.
Applications
of
the
Theorem
of
Peter
and
Wey1
5.
Generalizations
of
the
Theorem
of
Peter
and
Wey1
6.
Induced
Representations
7.
Tannaka-Krein
Duality
8.
The
Complexification
of
Compact
lie
CroupsCHAPTER

The
Maximal
Torus
of
a
Compact
Lie
Group
1.
Maximal
Tori
2.
Consequences
of
the
Conjugation
Theorem
3.
The
Maximal
Tori
and
Wey1
Groups
of
the
Classical
Groups
4.
Cartan
Subgroups
of
Nonconnected
Compact
GroupsCHAPTER

Root
SystemsCHAPTER

Irreducible
Characters
and
WeightsBibliographySymbol
IndexSubject
Index

图书封面

图书标签Tags

GTM,数学,Springer,表示论


    紧李群的表示下载



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