克裡斯編著的《表示論和復幾何（英文影印版）》是一部經典的從集合角度講述表示論的高等教程。從幾何的角度研究表示論，真可謂“千呼萬呼始出來”，尤其是自從1980年D-模型和1990年量子群的箭圖，此方法顯得*為迫切。表示論的發展順應科學發展趨勢，並且都成功地應用於好多領域，如量子群、仿射李群和量子場論。本書的前半部分是架起李理論標準知識初學者和數學工作者所需要的廣闊背景知識之間的橋梁，為後半部分的學習做好充分的準備。

preface
chapter 0. introduction
chapter 1. symplectic geometry
1.1. symplectic manifolds
1.2. poisson algebras
1.3. poisson structures arising from noncommutative algebras
1.4. the moment map
1.5. coisotropic subvarieties
1.6. lagrangian families
chapter 2. mosaic
2.1. hilbert's nullste!lensatz
2.2. atone algebraic varieties
2.3. the deformation construction
2.4. c*-actions on a projective variety
2.5. fixed point reduction
2.6. borel-moore homology
2.7. convolution in borel-moore homology
chapter 3. complex semisimple groups
3.1. semisimple lie algebras and flag varieties
3.2. nilpotent cone
3.3. the steinberg variety
3.4. lagrangian construction of the weyl group
3.5. geometric analysis of h(z)-action
3.6. irreducible representations of we~1 groups
3.7. applications of the jacobson-morozov theorem
chapter 4. springer theory for u(sln)
4.1. geometric construction of the enveloping algebra u(sin(c))
4.2. finite-dimensional simple sln(c)-modules
4.3. proof of the main theorem
4.4. stabilization
chapter 5. equivariant k-theory
5.1. equivariant resolutions
5.2. basic k-theoretic constructions
5.3. specialization in equivariant k-theory
5.4. the koszul complex and the thom isomorphism
5.5. cellular fibration lemma
5.6. the k/inneth formula
5.7. projective bundle theorem and beilinson resolution
5.8. the chern character
5.9. the dimension filtration and "devissage"
5.10. the localization theorem
5.11. functoriality
chapter 6. flag varieties, k-theory, and harmonic polynomials
6.1. equivariant k-theory of the flag variety
6.2. equivariant k-theory of the steinberg variety
6.3. harmonic polynomials
6.4. w-harmonic polynomials and flag varieties
6.5. orbital varieties
6.6. the equivariant hilbert polynomial
6.7. kostant's theorem on polynomial rings
chapter 7. hecke algebras and k-theory
7.1. affine weyl groups and hecke algebras
7.2. main theorems
7.3. case q = h deformation argument
7.4. hilbert polynomials and orbital varieties
7.5. the hecke algebra for sl2
7.6. pwof of the main theorem
chapter 8. representations of convolution algebras
8.1. standard modules
8.2. character formula for standard modules
8.3. constructible complexes
8.4. perverse sheaves and the classification theorem
8.5. the contravariant form
8.6. shed-theoretic analysis of the convolution algebra
8.7. projective modules over convolution algebra
8.8. a non-vanishing result
8.9. semi-small maps
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