Systems related to Group Theory
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
(Lehrstuhl D fuer Mathematik, RWTH Aachen) and
(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.
For more information we refer to the Chevie web-site.
- 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
Special Purpose Systems
Last updated: May 7, 1998