Contemporary Mathematics 1993; 259 pp; softcover Volume: 154 ISBN10: 0821851764 ISBN13: 9780821851760 List Price: US$60 Member Price: US$48 Order Code: CONM/154
 This book contains refereed papers presented at the AMSIMSSIAM 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  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 quaternionicKähler 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
