The Atlas of Lie Groups and Representations

The Atlas of Lie Groups and Representations is a project to make available information about representations semi-simple 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.

We have computed 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 is a some more technical details on what we really did.

Visit the atlas wiki

Version 0.2.6 of the Atlas software is now available from the software page. This computes structure and representation theory of real reductive groups, including Kazhdan-Lusztig-Vogan polynomials.

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. Currently this includes:

    Software, the Atlas software for computing structure theory and admissible representations of real groups,

    Papers, including notes of the Palo Alto workshops.

    Talks: slides from various public lectures, including David Vogan's lecture announcing the E₈ calculation, March 19, 2007

    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)

    Spherical Unitary Dual: tables of spherical unitary representations, including both classical and exceptional groups

    Models of representations of Weyl groups.

People who are working on the Atlas project.

Other web sites of interest. You might also browse the home pages of the Atlas people.

This work is supported by the NSF and the American Institute of Mathematics.

For more information see acknowledgements.