The GAP-part of CHEVIE

Important structures for the representation theory of finite groups of Lie type (and for other areas of mathematics as well) are the associated Weyl groups and Iwahori-Hecke algebras. The GAP part of CHEVIE deals, in a slightly more general way, with finite Coxeter groups and their Iwahori-Hecke algebras.

Below is an outline of this part of CHEVIE. It applies to the officially released version which is distributed as a share package with GAP-3.4.4. This version of GAP is no longer updated (but very stable and useful), therefore we don't have official new releases of the package.

Nevertheless, the package is further developed (mainly by Frank Lübeck and Jean Michel), there are much generalized concepts, new features and new data from current research. There is a development version of the GAP-3 package, mainly maintained by Jean Michel, and `soon' there will be a completely new package based on GAP-4, written by Frank Lübeck. With the official release one can

• create Coxeter groups by type, Cartan matrix or root datum, as well as reflection subgroups
• compute with their elements as permutations on a root system, matrices or words in the Coxeter generators
• get character tables of the Coxeter groups and induce/restrict matrices for (reflection) subgroups
• compute Macdonald-Lusztig-Spaltenstein $j$-induction and Lusztig's $J$-induction
• create and compute with "Coxeter cosets" and to get their character tables
• create braid groups and compute with their elements
• compute Bruhat orders, Kazhdan-Lusztig polynomials and left cells
• create Iwahori-Hecke algebras and compute with their elements in different bases: $T$_w, $C$_w, $C\text{'}$_w, $D$_w, $D\text{'}$_w
• get character tables of the Iwahori-Hecke algebras, reflection and left cell representations, Poincaré polynomials, Schur elements and generic degrees
• have preliminary support for complex reflection groups, cyclotomic algebras and Hecke cosets

For more information on this part of CHEVIE you can study the manual (in gzipped dvi format (100k) or in gzipped postscript format (164k)).

Back to CHEVIE's home or to the next section.

Last modified: Mon Jul 15 18:05:07 CEST 2001 by Frank Lübeck