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.
The workshop will be followed by a conference entitled Representation
Theory of Real Reductive Groups

The workshop is funded in part by MSRI, NSF Grant DMS-0554278, and
Utah's VIGRE grant.