Lorentz Center - Generalizations of Symmetric Spaces from 25 Nov 2013 through 29 Nov 2013
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    Generalizations of Symmetric Spaces
    from 25 Nov 2013 through 29 Nov 2013


Generalizations of Symmetric Spaces

25 – 29 November 2013 @Oort

The topic

Groups and their homogeneous spaces are basic objects in science and to unravel their structure and that of certain classes of functions on them is of fundamental importance. The key objects of study in the workshop were the classical symmetric spaces of real Lie groups, their p-adic and Kac-Moody generalizations and spherical varieties.

A unifying feature of these generalizations of symmetric spaces of non-compact type is that the acting groups admit a BN-pair, which leads to a deep interaction between the theory of (generalizations of) symmetric spaces on one hand and the theory of spherical, affine, and hyperbolic Tits buildings on the other hand. At the conference special emphasis was put on this interaction. It played a role in about one third of the lectures and there one could observe a real cross-fertilization: in certain cases, known results on the classical side formed the inspiration to look for analogues on the building side and reversely, properties of buildings could be used to prove results for symmetric spaces.


The program consisted of 22 addresses of 45 minutes each followed by lively discussions. The program possesed a number of leading threads, namely

1)    Geometric aspects of classical symmetric spaces,

2)    Representation theoretic questions for classical symmetric spaces,

3)    Representation theory related to p-adic symmetric spaces,

4)    Infinite dimensional symmetric spaces: Kac-Moody and beyond,

5)    Properties of various types of buildings.


The program was attended by 48 participants from Belgium, Denmark, France, Germany, Israel, Italy, Japan, the Netherlands, Russia and the US, showing the broad international interest in and character of the workshop. Among them there were five female researchers and a substantial group of young people.


Reactions at the end of the conference and afterwards at later encounters, were very positive: many participants told us that this workshop formed a source of inspiration for them, leading to new ideas and yielding various new cooperations that will result in joint papers and activities. E.g. during the conference concrete plans were developed for future follow-ups in the USA and Israel.

The conference was financially made possible by the support of the following institutions or organizations:

1)    The Lorentz Center (NWO)

2)    The Royal Dutch Academy of Sciences

3)    Foundation Compositio

Finally we like to express our gratitude to the staff of the Lorentz Center, in particular Henriette Jensenius, Mieke Schutte and Sietske Kroon for their guidance, help and support at the whole process of organizing this workshop. All participants were impressed by the pleasant ambiance at the Center and the excellent support from its staff.

Aloysius Helminck (Raleigh, USA)  

Gerard Helminck (Amsterdam, The Netherlands)  

Ralf Köhl (Giessen, Germany)