# Finite and Infinite Dimensional Complex Geometry and Representation Theory

### Alan T. Huckleberry

Ruhr-Universität Bochum, Germany### Karl-Hermann Neeb

Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany### Joseph Albert Wolf

University of California, Berkeley, USA

## Abstract

As the theme of the conference indicates, one of the organizers' main goals was to put together a group of participants with a wide range of interests in and around the complex geometric side of the representation theory of Lie groups and algebras. It is their belief that a hybrid approach to representation theory, in particular interaction between complex geometers and harmonic analysts standing on a strong foundation of finite- and infinite-dimensional Lie theory, will open up new avenues of thought and lead to progress in a number of areas. Since the previous Oberwolfach conference (Represention Theory and Complex Analysis, April 2000), there has been quite a positive development toward these goals. A number of breakthroughs were achieved, and of course these were reported at this year's conference. More than half of the 47 participants (from 15 countries) are now working in some middle ground between complex geometry and representation theory. Furthermore, it was clear from the discussions both after the talks and in the evenings that most participants now understand each other's language well enough to discuss high level research projects. A basic new component, infinite-dimensional complex geometry and related representation theory, was added this year. This quickly developing subject is already attracting wide attention. A goal for the future is to better integrate this with the more classical finite-dimensional theory. One consequence of the broad range of backgrounds of the participants is that, without prodding by the organizers, virtually all speakers gave quite comprehensive introductions to their subjects before going into their most recent results. This was greatly appreciated by all! Instead of attempting to summarize these talks we will let the following abstracts speak for themselves.

## Cite this article

Alan T. Huckleberry, Karl-Hermann Neeb, Joseph Albert Wolf, Finite and Infinite Dimensional Complex Geometry and Representation Theory. Oberwolfach Rep. 1 (2004), no. 1, pp. 295–348

DOI 10.4171/OWR/2004/06