The unitary dual
Computing the Unitary Dual
A primary goal of the Atlas of Lie Groups and Representations project is to compute the unitary dual of any real reductive group. This is now implemented in Version 2.0 of the Atlas software. We have used it compute the unitary dual of groups up to and including E7, and are currently working on E8.
The software also implements many other algorithms in the representation theory of real reductive groups. See Software for more information on what it can do.
Explore the site
- Software
Download and install atlas, the program behind the project.
- Software demosNew
Worked sessions showing what atlas can compute.
- AI + atlasNew
How to use Claude to run atlas for you.
- Documentation
Installation, tutorials, the command language and function reference.
- Papers
Research papers, preprints and workshop notes.
- Talks
Slides from talks by project members.
- Tables
Structure and representation-theoretic data for real groups.
- Workshops
Atlas workshops, with schedules and materials.
- People
The mathematicians who have built the atlas.
From the archive · 2007
Kazhdan–Lusztig–Vogan polynomials for E8
The project computed the Kazhdan–Lusztig–Vogan polynomials for the largest block of split real E8, which has 453,060 representations. The largest coefficient is 11,808,808.