**CHEVIE** is a joint project of

- Meinolf Geck (Aberdeen)
- Gerhard Hiß (Aachen)
- Frank Lübeck (Aachen)
- Gunter Malle (Kaiserslautern)
- Jean Michel (Paris)
- Götz Pfeiffer (Galway)

**CHEVIE** is a computer algebra package for symbolic calculations
with generic character tables of groups of Lie type, and related
mathematical structures: Weyl groups and Iwahori-Hecke algebras. It has
been extended to deal with some infinite Coxeter groups such as the affine
Weyl groups, and also to deal with groups generated by pseudo-reflections
in a complex vector space and the associated `cyclotomic Hecke algebras'
and braid groups. It is written partly in MAPLE, and partly in GAP3. This page concerns the latest developements of the
GAP part of CHEVIE. You should look at the CHEVIE homepage for
other information on CHEVIE.

The purpose of this page is to always give access to the latest developement version of the GAP part of CHEVIE; if you find some bugs, bad designs, etc... don't complain about them, or rather if you do, do it by sending Email to me.

Here is brief summary of what's new compared to the version CHEVIE 3.1 in the official version GAP 3.4.4 of 1997.

- Affine Weyl groups, general Coxeter groups, and the corresponding Hecke algebras (with the Kazhdan-Lusztig bases $C$ and $C\text{'}$ — $D$ and $D\text{'}$ are not yet implemented for infinite groups).
- Now any group isomorphic to a Coxeter group can be made into a Coxeter group (e.g. the symmetric group in its natural permutation representation).
- More support for generic programming with Coxeter groups: most routines are now written in terms of primitives FirstLeftDescending, LeftDescentSet, etc.. and work generically for arbitrary Coxeter groups whatever the representation (e.g. Affine Weyl groups elements are represented as matrices, instead of the permutations used for finite Coxeter groups).
- Some support for unequal-parameter Kazhdan-Lusztig polynomials and bases.
- Hecke modules on Hecke algebras of general Coxeter groups, including the Kazhdan-Lusztig bases defined by Deodhar and Soergel for these modules.
- The possibility of defining Coxeter Cosets corresponding to the `very twisted' Ree and Suzuki groups of Lie type. Together with affine Weyl groups, this corresponds to the possibility of starting with more general Cartan matrices than before.
- Reflection cosets for arbitrary complex reflection groups have also been implemented, together with their automatic classification.
- More Hecke algebras for complex reflexion groups (there are complete
character tables excepted for groups in the range G
_{31}to G_{34}where there are only partial tables). Quite a few methods work now for arbitrary finite complex reflection groups, such as type recognition (decomposition into a product of irreducible groups), so routines for e.g. character tables have become fast and accurate using such decompositions. - The actual representing matrices for representations of Hecke
algebras. Thank to data from various people (Alvis, Naruse, Howlett, Yin)
all representations of Hecke algebras for finite coxeter groups are in
CHEVIE, and thanks to work with Gunter Malle there are representing
matrices for cyclotomic algebras of all complex reflection groups, excepted
that there are only partial lists for the exceptional complex groups in the
range G
_{29}—G_{34}. - Braid monoids for general Coxeter groups, dual braid monoids for finite Coxeter groups and well-generated complex reflection groups, and general Garside and locally Garside monoids. The algorithms to determine conjugacy and compute centralizers in Garside groups of Franco, Gonzalez-Meneses and Gebhardt have been implemented.
- Semisimple elements of reductive groups, including the computation of centralizers, and determining the list of isolated and quasi-isolated classes.
- Unipotent characters for reductive groups and Spetses. Lusztig induction of unipotent characters and Lusztig's fourier trans has been implemented.
- Unipotent classes of reductive groups (including the bad
characteristic case) and the generalized Springer correspondence.
For more information you can look at the manual online.

## How to install this version of

To help people who are interested in CHEVIE or other GAP3 packages not ported to GAP4 I have prepared an easy-to install GAP3 distribution. I recommend to use this rather than trying to install CHEVIE separately, especially since CHEVIE depends for some functionalities on some other packages being up to date.**CHEVIE**onto your computer