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The Penrose Transform and Analytic Cohomology in Representation Theory
Edited by: Michael Eastwood, Joseph Wolf, and Roger Zierau
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Contemporary Mathematics
1993; 259 pp; softcover
Volume: 154
ISBN-10: 0-8218-5176-4
ISBN-13: 978-0-8218-5176-0
List Price: US$57 Member Price: US$45.60
Order Code: CONM/154

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.

Researchers and graduate students in representation theory and differential geometry.

• A. W. Knapp -- Introduction to representations in analytic cohomology
• J. A. Wolf -- Admissible representations and geometry of flag manifolds
• D. A. Vogan, Jr. -- Unipotent representations and cohomological induction
• M. Eastwood -- Introduction to Penrose transform
• L. Barchini -- Strongly harmonic differential forms on elliptic orbits
• C. LeBrun -- A finiteness theorem for quaternionic-Kähler manifolds with positive scalar curvature
• S. Gindikin -- Holomorphic language for $$\overline \partial$$-cohomology and representations of real semisimple Lie groups
• E. G. Dunne and R. Zierau -- Twistor theory for indefinite Kähler symmetric spaces
• D. Miličić -- Algebraic $${\mathcal D}$$-modules and representation theory of semisimple Lie groups
• T. N. Bailey -- Parabolic invariant theory and geometry
• M.-K. Chuah and V. Guillemin -- Kaehler structures on $$K_{\mathbb C}/N$$
• J. W. Rice -- Cousin complexes and resolutions of representations
• H. W. Wong -- Dolbeault cohomologies and Zuckerman modules
• D. Barbasch -- Unipotent representations and derived functor modules
• R. Zierau -- Unitarity of certain Dolbeault cohomology representations