This volume contains papers presented at the conference "The Penrose Trans-
form and Analytic Cohomology in Representation Theory," held 27th June to
3rd July, 1992, at Mount Holyoke College, South Hadley, Massachusetts. All art-
icles have been refereed. The conference was one of a series of Summer Research
Conferences sponsored jointly by the American Mathematical Society, the Institute
of Mathematical Statistics, and the Society for Industrial and Applied Mathemat-
ics, and supported by a grant from the National Science Foundation. The organ-
izing committee consisted of Robert J. Baston (Co-chair), Michael G. Eastwood
(Co-chair), Victor W. Guillemin, Joseph A. Wolf, and Roger Zierau.
The main idea of this conference was to bring together representation theorists
and differential geometers in order that they may profitably interact. In particular,
it seemed that various integral transforms from representation theory, complex
integral geometry, and mathematical physics were instances of the same general
construction sometimes called the "Penrose transform". Speakers were asked to
give talks bearing the diverse and non-specialist nature of their audience in mind.
In this respect and also in informal discussion, the conference was very successful.
There is considerable scope for further research and we hope that this conference
and its proceedings will be seen as a useful catalyst.
Generally speaking, the programme was arranged with the more expository talks
early on so that later speakers could refer to topics already discussed. The order has
been maintained in these proceedings. Unfortunately, Victor Guillemin was unable
to attend but has contributed a joint article with Meng-Kiat Chauh. Lisa Mantini
kindly agreed to speak in his place. The programme and list of participants is given
Special thanks are due to Carole Kohanski as Conference Coordinator and Donna
Harmon for Editorial Assistance.