**Contemporary Mathematics**

Volume: 154;
1993;
259 pp;
Softcover

MSC: Primary 22;
Secondary 32; 14; 53

Print ISBN: 978-0-8218-5176-0

Product Code: CONM/154

List Price: $60.00

AMS Member Price: $48.00

MAA Member Price: $54.00

**Electronic ISBN: 978-0-8218-7745-6
Product Code: CONM/154.E**

List Price: $60.00

AMS Member Price: $48.00

MAA Member Price: $54.00

# The Penrose Transform and Analytic Cohomology in Representation Theory

Share this page *Edited by *
*Michael Eastwood; Joseph Wolf; Roger Zierau*

This book contains refereed papers presented at the AMS-IMS-SIAM Summer Research Conference on the Penrose Transform and Analytic Cohomology in Representation Theory held in the summer of 1992 at Mount Holyoke College. The conference brought together some of the top experts in representation theory and differential geometry. One of the issues explored at the conference was the fact that various integral transforms from representation theory, complex integral geometry, and mathematical physics appear to be instances of the same general construction, which is sometimes called the “Penrose transform”. There is considerable scope for further research in this area, and this book serves as an excellent introduction.

#### Readership

Researchers and graduate students in representation theory and differential geometry.

# Table of Contents

## The Penrose Transform and Analytic Cohomology in Representation Theory

- Contents vii8 free
- Preface ix10 free
- Introduction to representations in analytic cohomology 112 free
- Admissible representations and geometry of flag manifolds 2132
- Unipotent representations and cohomological induction 4758
- Introduction to Penrose transform 7182
- Strongly harmonic differential forms on elliptic orbits 7788
- A finiteness theorem for quaternionic-Kähler manifolds with positive scalar curvature 89100
- Holomorphic language for ∂-cohomology and representations of real semisimple Lie groups 103114
- Twistor theory for indefinite Kähler symmetric spaces 117128
- Algebraic D-modules and representation theory of semisimpleLie groups 133144
- Parabolic invariant theory and geometry 169180
- Kaehler Structures on Kc/N 181192
- Cousin complexes and resolutions of representations 197208
- Dolbeault cohomologies and Zuckerman modules 217228
- Unipotent representations and derived functor modules 225236
- Unitarity of certain Dolbeault cohomology representations 239250