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.

The latest version of the software is 1.1. It is free and open source and runs on linux/Mac/Windows. Here are download and install instruction for the software, and a summary of features.
The Online Seminar on representation theory and the Atlas software is starting on January 6, 2022. This is an introduction to representations of real groups and the software and will be accessible to a broad audience.
There is a Slack Worskspace for discussing the software. Click on this link to join. Use this workspace for questions and discussions about all aspects of the Atlas software.

Here are the main parts of the Atlas web site:

Software:   The atlas software runs on linux, Mac and Windows. The source code is freely available, and it can also be run using Docker. See download and install instructions from the documentation section of the site.
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 section of the 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
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.

Support for the Atlas project