Unitary Representations of Reductive Lie Groups
Published on 21. October 1987
Book
Paperback/Softback
319 pages
978-0-691-08482-4 (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.
More details
Series
Language
English
Place of publication
New Jersey
United States
Target group
Professional and scholarly
College/higher education
Product notice
Paperback (trade)
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 19 mm
Weight
522 gr
ISBN-13
978-0-691-08482-4 (9780691084824)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
David A. Vogan
Unitary Representations of Reductive Lie Groups
E-Book
06/2016
1st Edition
Princeton University Press
€122.99
Available for download
Person
David A. Vogan Jr.
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