As part of the Atlas project we are developing software to compute structure theory and representations of real reductive groups. Fokko du Cloux was the lead programmer on this project from 2002 to 2006. This role has been assumed by Marc van Leeuwen. Here is where you will find this software and other information.

The software is in an early stage of development. You may input

• a general connected complex reductive group G;
• an inner class of strong real forms of G;
• a real form of G.

• the component group of G;
• the conjugacy classes of Cartan subgroups of G;
• the ("real") Weyl group of each Cartan subgroup;
• parameters for the irreducible representations of G with regular integral infinitesimal character;
• gradings of roots (compact imaginary, non-compact imaginary, parity condition, etc.);
• the cross action and Cayley transforms of irreducible characters;
• Kazhdan-Lusztig polynomials for representations with regular integral infinitesimal character.
• The W-graph associated to irreducible characters, and the Kazhdan-Lusztig W-cells of representations.
• The Bruhat order on a block of irreducible representations.

Software | Atlas Home Page