Unitary Representations of Reductive Lie Groups
1st Edition
Published on 20. June 2016
319 pages
978-1-4008-8238-0 (ISBN)
Description
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.
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.
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David A. Vogan
Unitary Representations of Reductive Lie Groups
Book
10/1987
Princeton University Press
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David A. Vogan
Unitary Representations of Reductive Lie Groups
Book
10/1987
Princeton University Press
€97.50
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Content
Frontmatter, pg. i
CONTENTS, pg. vii
ACKNOWLEDGEMENTS, pg. ix
INTRODUCTION, pg. 1
Chapter 1. COMPACT GROUPS AND THE BOREL-WEIL THEOREM, pg. 19
Chapter 2. HARISH-CHANDRA MODULES, pg. 50
Chapter 3. PARABOLIC INDUCTION, pg. 62
Chapter 4. STEIN COMPLEMENTARY SERIES AND THE UNITARY DUAL OF GL(n,C), pg. 82
Chapter 5. COHOMOLOGICAL PARABOLIC INDUCTION: ANALYTIC THEORY, pg. 105
Chapter 6. COHOMOLOGICAL PARABOLIC INDUCTION: ALGEBRAIC THEORY, pg. 123
Interlude. THE IDEA OF UNIPOTENT REPRESENTATIONS, pg. 159
Chapter 7. FINITE GROUPS AND UNIPOTENT REPRESENTATIONS, pg. 164
Chapter 8. LANGLANDS' PRINCIPLE OF FUNCTORIALITY AND UNIPOTENT REPRESENTATIONS, pg. 185
Chapter 9. PRIMITIVE IDEALS AND UNIPOTENT REPRESENTATIONS, pg. 211
Chapter 10. THE ORBIT METHOD AND UNIPOTENT REPRESENTATIONS, pg. 235
Chapter 11. E-MULTIPLICITIES AND UNIPOTENT REPRESENTATIONS, pg. 258
Chapter 12. ON THE DEFINITION OF UNIPOTENT REPRESENTATIONS, pg. 284
Chapter 13. EXHAUSTION, pg. 290
REFERENCES, pg. 302
Backmatter, pg. 309
CONTENTS, pg. vii
ACKNOWLEDGEMENTS, pg. ix
INTRODUCTION, pg. 1
Chapter 1. COMPACT GROUPS AND THE BOREL-WEIL THEOREM, pg. 19
Chapter 2. HARISH-CHANDRA MODULES, pg. 50
Chapter 3. PARABOLIC INDUCTION, pg. 62
Chapter 4. STEIN COMPLEMENTARY SERIES AND THE UNITARY DUAL OF GL(n,C), pg. 82
Chapter 5. COHOMOLOGICAL PARABOLIC INDUCTION: ANALYTIC THEORY, pg. 105
Chapter 6. COHOMOLOGICAL PARABOLIC INDUCTION: ALGEBRAIC THEORY, pg. 123
Interlude. THE IDEA OF UNIPOTENT REPRESENTATIONS, pg. 159
Chapter 7. FINITE GROUPS AND UNIPOTENT REPRESENTATIONS, pg. 164
Chapter 8. LANGLANDS' PRINCIPLE OF FUNCTORIALITY AND UNIPOTENT REPRESENTATIONS, pg. 185
Chapter 9. PRIMITIVE IDEALS AND UNIPOTENT REPRESENTATIONS, pg. 211
Chapter 10. THE ORBIT METHOD AND UNIPOTENT REPRESENTATIONS, pg. 235
Chapter 11. E-MULTIPLICITIES AND UNIPOTENT REPRESENTATIONS, pg. 258
Chapter 12. ON THE DEFINITION OF UNIPOTENT REPRESENTATIONS, pg. 284
Chapter 13. EXHAUSTION, pg. 290
REFERENCES, pg. 302
Backmatter, pg. 309
