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连续上同调、离散子群与约化群表示，第二版（影印版）

样章
作者：
A. Borel，N. Wallach
定价：
135.00 元
版面字数：
483千字
开本：
16开
装帧形式：
精装
版次：
1
最新版次
印刷时间：
2021年
ISBN：
978-7-04-055637-7
物料号：
55637-00
出版时间：
2021-03-03
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
代数学
暂无
  • 目录
    • 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(Γ\G)
                                                                                                                            • 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

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