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Unitary Representations of Reductive Lie Groups

✍ Scribed by David A. Vogan

Publisher
Princeton University Press
Year
1987
Tongue
English
Leaves
319
Series
Annals of Mathematics Studies 118
Category
Library
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✦ Synopsis


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.


✦ Table of Contents

Content: Frontmatter, pg. iCONTENTS, pg. viiACKNOWLEDGEMENTS, pg. ixINTRODUCTION, pg. 1Chapter 1. COMPACT GROUPS AND THE BOREL-WEIL THEOREM, pg. 19Chapter 2. HARISH-CHANDRA MODULES, pg. 50Chapter 3. PARABOLIC INDUCTION, pg. 62Chapter 4. STEIN COMPLEMENTARY SERIES AND THE UNITARY DUAL OF GL(n,C), pg. 82Chapter 5. COHOMOLOGICAL PARABOLIC INDUCTION: ANALYTIC THEORY, pg. 105Chapter 6. COHOMOLOGICAL PARABOLIC INDUCTION: ALGEBRAIC THEORY, pg. 123Interlude. THE IDEA OF UNIPOTENT REPRESENTATIONS, pg. 159Chapter 7. FINITE GROUPS AND UNIPOTENT REPRESENTATIONS, pg. 164Chapter 8. LANGLANDS' PRINCIPLE OF FUNCTORIALITY AND UNIPOTENT REPRESENTATIONS, pg. 185Chapter 9. PRIMITIVE IDEALS AND UNIPOTENT REPRESENTATIONS, pg. 211Chapter 10. THE ORBIT METHOD AND UNIPOTENT REPRESENTATIONS, pg. 235Chapter 11. E-MULTIPLICITIES AND UNIPOTENT REPRESENTATIONS, pg. 258Chapter 12. ON THE DEFINITION OF UNIPOTENT REPRESENTATIONS, pg. 284Chapter 13. EXHAUSTION, pg. 290REFERENCES, pg. 302Backmatter, pg. 309

✦ Subjects

Lie groups;Representations of groups;Groupes de Lie;Représentations de groupes;Lie, Groupes de;groupes de Lie réductifs -- représentations unitaires

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