Atlas of Lie Groups and Representations

The Atlas of Lie Groups and Representations software is useful for doing computations with representation theory of real reductive groups. Here is a brief description of the current state of the software (November 2013).

The software allows the user to define an arbitrary reductive group, and gives access to its root data. The user can also define an arbitrary real form G of such a group. The user can define a parameter for an arbitrary irreducible admissible representation of G, and the software will compute its block, Cayley transforms, cross actions, and Kazhdan-Lusztig-Vogan polynomials. In particular this includes character formulas (for irreducible representations) and composition series (for standard modules).

The software computes the signature of the invariant Hermitian form on an irreducible representation pi, and therefore can determine if pi is unitary. See Mathematical Background, and for complete details see Unitary representations of real reductive groups.

Here is more detail on the capabilities of the software.

Download and Install the Atlas software

A Web Interface to the software is available, although this is quite behind the current state of the software itself.

The original software was written by Fokko du Cloux. In November 2006 Marc van Leeuwen took over primary responsibility for the code.

Here is more information on what the software does, and some examples of how to use it. See the tables of data produced using the software.

Copyright and license information

Fokko du Cloux's coxeter software, for computing Kazhdan-Lusztig polynomials for Coxeter groups, is now available here.