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 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.

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.

You may have heard about our computation 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 are some more technical details on what we really did.

The atlas software runs under unix, and is freely available from the software page.
NEW: A web interface to the atlas software is now available.

Here are the main parts of the Atlas web site:

Software:  The primary Atlas software is in an early stage of development, currently version 0.4. It is freely available. Other helper applications which work with the atlas software are also available.

Web interface to the atlas software.

Papers:    Expository notes, notes of lectures, etc.

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

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:    Tables computed using the Atlas and associated software. Includes:
   Structure theory of Lie groups
   Representation theory of Lie groups
  
Spherical unitary representations
   Unipotent Orbits
   Unipotent Representations
   Models of representations of Weyl groups.

Atlas wiki:  public wiki for discussion of the atlas project

People who are working on the Atlas project.


This work is supported by the NSF and the American Institute of Mathematics. For more information see the acknowledgements.