Atlas of Lie Groups and Representations

The Atlas of Lie Groups and Representations is a project to make available information about representations of reductive Lie groups over real and p-adic fields. Of particular importance is the problem of the unitary dual: classifying all of the irreducible unitary representations of a given Lie group.

The Atlas consists in part of a project to compute the unitary dual, by mathematical and computational methods. We are also planning to make information about Lie groups and representation theory, in particular unitary representations, available to the general mathematical public.

Computing Unitary Representations The Atlas software can now compute if any irreducible admissible representation of a real reductive group is unitary. This completes a main goal of the project. Version 1.0 of the software will be released soon.
Atlas Workshop There will be a workshop on the Atlas project at the University of Utah, July 10-21. Some funding is available. More details will be provided soon.
Atlas Documentation The new documentation web site is now available. It has help installing and running the software, and explanations and examples of many atlas commands. (More information is being added all the time.)
TwitterThe Atlas project has a Twitter feed. Follow us @atlas_liegroups to get (infrequent) announcements about the software

Here are the main parts of the Atlas web site:

Software:   The atlas software comes in linux and Mac versions. We recommend you compile it yourself, but you can try an precompiled binary. There is also a windows version.
Web interface to the atlas software. Development of the interface is running considerably behind the software itself, but we are currently working on a greatly improved version.
Talks: Slides from various public lectures, including David Vogan's lecture announcing the E8 calculation, March 19, 2007
2009 Workshop and conference web sites.
2013 Workshop and conference web sites.
2016 Japan Workshop
Spherical Unitary Explorer: an interactive tool for learning about spherical unitary representations of classical groups
Root Systems: A tool for viewing information about root systems (used with the Spherical Unitary Explorer)
Tables of data computed using the Atlas and associated software:
Structure theory of Lie groups
Representation theory of Lie groups
Spherical unitary representations
Unipotent Orbits
Unipotent Representations
Models of representations of Weyl groups
Galois cohomology of real groups.

You may have heard about our computation Kazhdan-Lusztig polynomials for the split real group E8. Here are some details of the calculation, and David Vogan has written a narrative of the project. There is an introduction to the calculation at AIM. For more information on the E8 calculation there are some slides of talks available in the talks section. Also see David Vogan's home page, and here are some more technical details on what we really did. People who are working on the Atlas project.

This work is supported by the NSF. For more information see the acknowledgements.