chapter ⅰ
lie grou and lie algebras
1.the concept of a lie group and the classical examples
2.left—invariant vector fields and one—parameter grou
3.the exponential map
4.homogeneous spaces and quotient grou
5.invariant integration
6.clifford algebras and spinor grou
chapter ⅱ
elementary representation theory
1.representations
2.semisimple modules
3.linear algebra and representations
4.characters and ortho sonality 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.representation of abelian grou
9.representations of lie algebras
10.the lie algebra sl（2，c）
chapter ⅲ
representative functions
1.algebras of representative functions
2.some analysis on pact grou
3.the theorem of peter and weyl
4.applications of the theorem of peter and weyl
5.generalizations of the theorem of peter and weyl
6.induced representations
7.tannaka—krein duality
8.the plefication of pact lie grou
chapter ⅳ
the mamal torus of a pact lie group
1.mamal tori
2.consequences of the conjugation theorem
3.the mamal tori and weyl grou of the classical grou
4.cartan subgrou of nonconnected pact orou
chapter ⅴ
root systems
1.the adjoint representation and grou of rank i
2.roots and weyl chambers
3.root systems
4.bases and weyl chambers
5.dynkin diagrams
6.the roots of the classical grou
7.the fundamental group， the center and the stiefel diagram
8.the structure of the pact c，rou
chapter ⅵ
irreducible characters and weights
1.the weyl character formula
2.the dominant weight and the structure of the representation ring
3.the multiplicities of the weights of an irreducible representation
4.representations of real or quatemionic type
5.representations of the classical grou
6.representations of the spinor grou
7.representations of the orthogonal grou
bibliography
symbol index
subject index
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