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. Of particular importance is the problem of the unitary dual: classifying all of the irreducible unitary representations of a given Lie group.

The Atlas software, which is freely available, can be used to do computations in Lie theory, from basic structure through computing unitary representations. Here are some references regarding the mathematical background of the software.

News
Computing Unitary Representations Version 1.0 of the Atlas software is now available. The software can now compute if any irreducible admissible representation of a real reductive group is unitary. This completes a main goal of the project.
Atlas Workshop A workshop on the Atlas project was held July 10-21. Slides of some of the talks as is video of every talk, as well as copies of the computer input/output for some of the talks.
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 a and PC versions. We recommend you compile it yourself, but you can try an precompiled binary.
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.
Papers:   Many notes and preprints related to the project. Some of these are of interest to the general user, and some only for experts. Much of the more elementary material can now be found on the documentation web site. Some of the more advanced material is in the notes from a series of workshops at AIM
Talks: Slides from various public lectures, including David Vogan's lecture announcing the E8 calculation, March 19, 2007
Workshops
2017 Workshop
2016 Japan Workshop
2013 Workshop and conference web sites.
2009 Workshop and conference web sites.
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.
People who are working on the Atlas project.

You may have heard about our computation Kazhdan-Lusztig polynomials for the split real group E8. Here are some details of the calculation, David Vogan has written a narrative of the project, and here are some more technical details on what we really did.


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