## 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 This version of GAP is no longer updated (but very stable and useful), therefore we don't have official new releases of the package.

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