Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118 / David A. Vogan.

Format:

Book

Author/Creator:

Vogan, David A., author.

Series:

Annals of mathematics studies ; no. 118.

Annals of Mathematics Studies ; 349

Language:

English

Subjects (All):

Lie groups.

Representations of Lie groups.

Physical Description:

1 online resource (320 pages)

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs. The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction. This culminates in the description of all irreducible unitary representation of the general linear groups. For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations.

Contents:

Frontmatter

CONTENTS

ACKNOWLEDGEMENTS

INTRODUCTION

Chapter 1. COMPACT GROUPS AND THE BOREL-WEIL THEOREM

Chapter 2. HARISH-CHANDRA MODULES

Chapter 3. PARABOLIC INDUCTION

Chapter 4. STEIN COMPLEMENTARY SERIES AND THE UNITARY DUAL OF GL(n,ℂ)

Chapter 5. COHOMOLOGICAL PARABOLIC INDUCTION: ANALYTIC THEORY

Chapter 6. COHOMOLOGICAL PARABOLIC INDUCTION: ALGEBRAIC THEORY

Interlude. THE IDEA OF UNIPOTENT REPRESENTATIONS

Chapter 7. FINITE GROUPS AND UNIPOTENT REPRESENTATIONS

Chapter 8. LANGLANDS' PRINCIPLE OF FUNCTORIALITY AND UNIPOTENT REPRESENTATIONS

Chapter 9. PRIMITIVE IDEALS AND UNIPOTENT REPRESENTATIONS

Chapter 10. THE ORBIT METHOD AND UNIPOTENT REPRESENTATIONS

Chapter 11. E-MULTIPLICITIES AND UNIPOTENT REPRESENTATIONS

Chapter 12. ON THE DEFINITION OF UNIPOTENT REPRESENTATIONS

Chapter 13. EXHAUSTION

REFERENCES

Backmatter

Notes:

Bibliographic Level Mode of Issuance: Monograph

Bibliography.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400882380

1400882389

OCLC:

979970578