Cohomological Induction and Unitary Representations (PMS-45), Volume 45

by Anthony W. Knapp, David A. Vogan Jr.

Overview

This book offers a systematic treatment--the first in book form--of the development and use of cohomological induction to construct unitary representations. George Mackey introduced induction in 1950 as a real analysis construction for passing from a unitary representation of a closed subgroup of a locally compact group to a unitary representation of the whole group. Later a parallel construction using complex analysis and its associated co-homology theories grew up as a result of work by Borel, Weil, Harish-Chandra, Bott, Langlands, Kostant, and Schmid. Cohomological induction, introduced by Zuckerman, is an algebraic analog that is technically more manageable than the complex-analysis construction and leads to a large repertory of irreducible unitary representations of reductive Lie groups.


The book, which is accessible to students beyond the first year of graduate school, will interest mathematicians and physicists who want to learn about and take advantage of the algebraic side of the representation theory of Lie groups. Cohomological Induction and Unitary Representations develops the necessary background in representation theory and includes an introductory chapter of motivation, a thorough treatment of the "translation principle," and four appendices on algebra and analysis.

Product Details

ISBN-13:	9781400883936
Publisher:	Princeton University Press
Publication date:	06/02/2016
Series:	Princeton Mathematical Series , #86
Sold by:	Barnes & Noble
Format:	eBook
Pages:	968
File size:	37 MB
Note:	This product may take a few minutes to download.

About the Author

Anthony W. Knapp is Professor of Mathematics at the State University of New York at Stony Brook. David A. Vogan, Jr., is Professor of Mathematics at the Massachusetts Institute of Technology.

Table of Contents

Preface

Prerequisites by Chapter

Standard Notation

Introduction

I Hecke Algebras

II The Category C(g, K)

III Duality Theorem

IV Reductive Pairs

V Cohomological Induction

VI Signature Theorem

VII Translation Functors

VIII Irreducibility Theorem

IX Unitarizability Theorem

X Minimal K Types

XI Transfer Theorem

XII Epilog: Weakly Unipotent Representations

App. A. Miscellaneous Algebra

App. B. Distributions on Manifolds

App. C. Elementary Homological Algebra

App. D. Spectral Sequences

Notes

References

Index of Notation

Index

Editorial Reviews

"This book is a thorough and excellent presentation of the 'cohomological' approach to the construction and classification of irreducible representations of semisimple real Lie groups."

Zentralblatt fòr Mathematik

Winner of the 1996 Award for Best Professional/Scholarly Book in Mathematics, Association of American Publishers

From the Publisher

"This book is a thorough and excellent presentation of the 'cohomological' approach to the construction and classification of irreducible representations of semisimple real Lie groups."

Zentralblatt fòr Mathematik

"This book is a thorough and excellent presentation of the 'cohomological' approach to the construction and classification of irreducible representations of semisimple real Lie groups."

Zentralblatt fur Mathematik