Computational Theory of Real
Reductive Groups A workshop, July 20-24, 2009, at the University of Utah |
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The structure of real reductive algebraic groups is controlled by a remarkably simple combinatorial framework, generalizing the presentation of Coxeter groups by generators and relations. This framework in turn makes much of the infinite-dimensional representation theory of such groups amenable to computation. The Atlas of Lie Groups and Representations project is devoted to looking at representation theory from this computationally informed perspective. The group (particularly Fokko du Cloux and Marc van Leeuwen) has written computer software aimed at supporting research in the field, and at helping those who want to learn the subject. The workshop will explore this point of view in lecture series aimed especially at graduate students and postdocs with only a modest background (such as the representation theory of compact Lie groups). Topics include: -
background on infinite dimensional representations of real
reductive groups; - geometry of orbits of symmetric subgroups on the flag variety;
- Kazhdan-Lusztig theory;
- approaches to the classification of unitary representations;
- geometry of the nilpotent cone.
Theory of Real Reductive Groups. The workshop is funded in part by MSRI, NSF Grant DMS-0554278, and Utah's VIGRE grant. |