Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups. (AM-94)

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The material presented here divides naturally into two parts, one devoted mainly to real Lie groups, the other to locally compact totally disconnected groups, in particular reductive p-adic groups, or products of real Lie groups and t.d. groups.
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More About This Book

Overview

The material presented here divides naturally into two parts, one devoted mainly to real Lie groups, the other to locally compact totally disconnected groups, in particular reductive p-adic groups, or products of real Lie groups and t.d. groups.
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Editorial Reviews

Booknews
Deals with two types of cohomology spaces pertaining to reductive Lie group and a discrete cocompact subgroup. Material presented here naturally divides into two parts, one devoted mainly to real Lie groups, the other to locally compact totally disconnected groups, in particular reductive

-adic groups, or products of real Lie groups and totally disconnected groups. Each part in turn contains roughly three main items: general results on the cohomology used, specific results for cohomology and representations of reductive groups, and applications to discrete cocompact subgroups. This second edition reports on developments in the field since 1980. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780691082493
  • Publisher: Princeton University Press
  • Publication date: 2/1/1980
  • Series: Annals of Mathematics Studies Series, #94
  • Pages: 398
  • Product dimensions: 5.94 (w) x 9.04 (h) x 1.03 (d)

Table of Contents

Introduction to the First Edition
Introduction to the Second Edition
Ch. 0 Notation and Preliminaries 1
Ch. I Relative Lie Algebra Cohomology 7
Ch. II Scalar Product, Laplacian and Casimir Element 31
Ch. III Cohomology with Respect to an Induced Representation 59
Ch. IV The Langlands Classification and Uniformly Bounded Representations 75
Ch. V Cohomology with Coefficients in II[subscript [infinity]](G) 97
Ch. VI The Computation of Certain Cohomology Groups 115
Ch. VII Cohomology of Discrete Subgroups and Lie Algebra Cohomology 137
Ch. VIII The Construction of Certain Unitary Representations and the Computation of the Corresponding Cohomology Groups 151
Ch. IX Continuous Cohomology and Differentiable Cohomology 169
Ch. X Continuous and Differentiable Cohomology for Locally Compact Totally Disconnected Groups 191
Ch. XI Cohomology with Coefficients in II[subscript [infinity]](G): The p-adic Case 211
Ch. XII Differentiable Cohomology for Products of Real Lie Groups and T.D. Groups 225
Ch. XIII Cohomology of Discrete Cocompact Subgroups 233
Ch. XIV Non-cocompact S-arithmetic Subgroups 247
Bibliography 253
Index 259
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