图书信息
图书目录
连续上同调、离散子群与约化群表示，第二版（影印版）
暂无简介
作者：
A. Borel，N. Wallach
定价：
135.00元
出版时间：
2021-03-03
ISBN：
978-7-04-055637-7
物料号：
55637-00
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
重点项目：
暂无
版面字数：
483.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
- 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
