Atlas Software
The Atlas software computes structure theory and admissible representations of real reductive groups. Originally written by Fokko du Cloux; primary development since 2006 by Marc van Leeuwen.
What the software does
Define an arbitrary reductive group and access its root data. Define a real form G and a parameter for any irreducible admissible representation. Compute its block, Cayley transforms, cross actions, and Kazhdan–Lusztig–Vogan polynomials — including character formulas and composition series for standard modules.
The software computes the signature of the invariant Hermitian form on a representation to determine whether it is unitary. See the Mathematical Background or the paper Unitary representations of real reductive groups.
Current version
Version 0.2.6 is now available. The software is open source, hosted on GitHub, and licensed under the GPL.
A web interface to the software is available, though it lags behind the current command-line version. Fokko du Cloux's Coxeter software for computing Kazhdan–Lusztig polynomials for Coxeter groups is also available here.
Download & Install
The software can be compiled from source or run via Docker (recommended for most users on macOS and Windows).
Capabilities & Examples
Capabilities
Detailed description of all computations the software supports, including all commands and algorithms.
Read more →Examples
Worked examples using the Atlas software on specific groups and representations.
See examples →Documentation
Full documentation including tutorial videos, the Axis language reference, and the built-in function index.
Open docs →Copyright & License
The Atlas software is free software distributed under the GNU General Public License. See the full license information. The original software was written by Fokko du Cloux (1954–2006). Marc van Leeuwen has been the primary developer since November 2006.