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 This version of **GAP** is no longer updated (but very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.

A development
version of the **GAP**-3 package, maintained by Jean Michel,
contains new features and new data from current research.

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: Fri, 04 Mar 2016 16:15:56 +0100 by Frank Lübeck