前辅文
Introduction to the First Edition
Introduction to the Second Edition
Chapter 0. Notation and Preliminaries
1. Notation
2. Representations of Lie groups
3. Linear algebraic and reductive groups
Chapter I. Relative Lie Algebra Cohomology
1. Lie algebra cohomology
2. The Ext functors for (g, k)-modules
3. Long exact sequences and Ext
4. A vanishing theorem
5. Extension to (g,K)-modules
6. (g, k, L)-modules. A Hochschild-Serre spectral sequence in the relative case
7. Poincar´e duality
8. The Zuckerman functors
Chapter II. Scalar Product, Laplacian and Casimir Element
1. Notation and general remarks
2. Scalar product
3. Special cases
4. The bigrading in the bounded symmetric domain case
5. Cohomology with respect to square integrable representations
6. Spinors and the spin Laplacian
7. Vanishing theorems using spinors
8. Matsushima’s vanishing theorem
9. Direct products
10. Sharp vanishing theorems
Chapter III. Cohomology with Respect to an Induced Representation
1. Notation and conventions
2. Induced representations and their K-finite vectors
3. Cohomology with respect to principal series representations
4. Fundamental parabolic subgroups
5. Tempered representations
6. Representations induced from tempered ones
7. Appendix: C∞ vectors in certain induced representations
Chapter IV. The Langlands Classification and Uniformly Bounded Representations
1. Some results of Harish-Chandra
2. Some ideas of Casselman
3. The Langlands classification (first step)
4. The Langlands classification (second step)
5. A necessary condition for uniform boundedness
6. Appendix: Langlands’ geometric lemmas
7. Appendix: A lemma on exponential polynomial series
Chapter V. Cohomology with Coefficients in Π∞(G)
1. Preliminaries
2. The class Π∞(G)
3. A vanishing theorem for the class Π∞(G)
4. Cohomology with coefficients in the Steinberg representation
5. H1 and the topology of E(G)
6. A more detailed examination of first cohomology
Chapter VI. The Computation of Certain Cohomology Groups
0. Translation functors
1. Cohomology with respect to minimal non-tempered representations. I
2. Cohomology with respect to minimal non-tempered representations. II
3. Semi-simple Lie groups with R-rank 1
4. The groups SO(n, 1) and SU(n, 1)
5. The Vogan-Zuckerman theorem
Chapter VII. Cohomology of Discrete Subgroups and Lie Algebra Cohomology
1. Manifolds
2. Discrete subgroups
3. Γ cocompact, E a unitary Γ-module
4. G semi-simple, Γ cocompact, E a unitary Γ-module
5. Γ cocompact, E a G-module
6. G semi-simple, Γ cocompact, E a G-module
Chapter VIII. The Construction of Certain Unitary Representations and the Computation of the Corresponding Cohomology Groups
1. The oscillator representation
2. The decomposition of the restriction of the oscillator representation to certain subgroups
3. The theta distributions
4. The reciprocity formula
5. The imbedding of Vl into L2(ΓG)
Chapter IX. Continuous Cohomology and Differentiable Cohomology
Introduction
1. Continuous cohomology for locally compact groups
2. Shapiro’s lemma
3. Hausdorff cohomology
4. Spectral sequences
5. Differentiable cohomology and continuous cohomology for Lie groups
6. Further results on differentiable cohomology
Chapter X. Continuous and Differentiable Cohomology for Locally Compact Totally Disconnected Groups
1. Continuous and smooth cohomology
2. Cohomology of reductive groups and buildings
3. Representations of reductive groups
4. Cohomology with respect to irreducible admissible representations
5. Forgetting the topology
6. Cohomology of products
Chapter XI. Cohomology with Coefficients in Π∞(G): The p-adic Case
1. Some results of Harish-Chandra
2. The Langlands classification (p-adic case)
3. Uniformly bounded representations and Π∞(G)
4. Another proof of the non-unitarizability of the VJ ’s
Chapter XII. Differentiable Cohomology for Products of Real Lie Groups and T.D. Groups
0. Homological algebra over idempotented algebras
1. Differentiable cohomology
2. Modules of K-finite vectors
3. Cohomology of products
Chapter XIII. Cohomology of Discrete Cocompact Subgroups
1. Subgroups of products of Lie groups and t.d. groups
2. Products of reductive groups
3. Irreducible subgroups of semi-simple groups
4. The Γ-module E is the restriction of a rational G-module
Chapter XIV. Non-cocompact S-arithmetic Subgroups
1. General properties
2. Stable cohomology
3. The use of L2 cohomology
4. S-arithmetic subgroups
Bibliography
Index
