Systems related to Group Theory

CHEVIE

CHEVIE is a computer algebra package for symbolic calculations with generic character tables of groups of Lie type (including Green functions), Weyl groups and Hecke algebras. It is based on the computer algebra systems GAP (Lehrstuhl D fuer Mathematik, RWTH Aachen) and Maple (The Symbolic Computation Group, University of Waterloo).

CHEVIE is accompanied by a library of generic character tables, tables of Green functions, tables of unipotent characters and character tables of Hecke algebras. Here is a brief sketch of the main features and contents of CHEVIE.

• Generic ordinary character tables for all series of finite groups of Lie type of small rank.
• Tables of Green polynomials (for exceptional and classical groups of low rank, and disconnected groups), and a program for calculating the Green polynomials for groups of type A.
• Programs for working with these tables (scalar products, tensor products, structure constants), constructing new tables and viewing respectively printing them in TeX format.
• Character tables of Hecke algebras for all types of rank at most 7, and recursive algorithms for computing them for types A and B (the formulae for type B and rank larger than 7 give the correct result only conjecturally). Tables and programs for the Weyl groups themselves are already available through GAP.
• Programs for computing Kazhdan-Lusztig polynomials, left cells and the corresponding representations for Weyl groups (effective for rank at most 4).
• A manual with a detailed description of the functions and illustrating examples.

Special Purpose Systems

Last updated: May 7, 1998