The Atlas of Lie Groups and Representations

This is the home page for the Atlas of Lie Groups and Representations. This 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.

NEW: We have computed Kazhdan-Lusztig polynomials for the split real group E₈. The largest coefficient which occurs is 11,808,808. Here are some details of the calculation, and David Vogan has written a narrative of the project.

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 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.

    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.

For information on support of this project see the acknowledgements