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Workshop on The Atlas of Lie Groups and Representations
July 10-21, 2017

Recently a combination of algebraic, geometric, and computational techniques have led to significant advances in the study of unitary representations of reductive Lie groups. The Atlas of Lie Groups and Representations is a project to compute the unitary dual of a real reductive group.

The project has reached a milestone: it now implements an algorithm to compute the signature of the invariant Hermitian form on an irreducible representation. In particular it can determine if any given irreducible representation is unitary.

The workshop will be devoted to the mathematics behind the algorithm, the algorithm itself, and its implementation. Topics include:

  • Structure theory of real reductive groups
  • The Langlands classfication
  • Kazhdan-Lusztig-Vogan theory
  • Hermitian and c-invariant forms
  • Twisted Kazhdan-Lusztig-Vogan theory
  • Computing signs of Hermitian forms
  • Applications
  • Open problems.

The algorithms have been implemented in computer software written by Fokko du Cloux and Marc van Leeuwen, aimed at supporting research in the field and at helping those who want to learn the subject. The workshop will include sessions using the software with a view toward attacking open problems.

Prospective participants please register here.

Some support is available. The workshop is supported by the NSF.