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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
ISBN：
978-7-04-055637-7
版面字数：
483.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
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
  • 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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