Homepage of the developement version of the GAP part of CHEVIE

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 more general information on CHEVIE.

The GAP part of CHEVIE

The purpose of this page is to always give access to the latest developement version (or should I say alpha version) of the GAP part of CHEVIE; so you can expect some bugs, temporary 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 latest released version, CHEVIE 3.1 distributed with GAP 3.4.4.

• 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). 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)
• Some (yet limited) support for unequal-parameter Kazhdan-Lusztig polynomials and bases.
• 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).
• 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.
• More Hecke algebras for complex reflexion groups (the only missing character tables are a few exceptional groups). 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 only some of the exceptional complex groups in the range G₂₉—G₃₄ are missing.
• 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.

  For more information you can download the manual of the developement version (dvi or pdf) or peruse the manual online.

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  How to install the developement version of CHEVIE onto your computer

  A pre-packaged GAP3 with everything you need

  To help people who are just interested in CHEVIE or VKCURVE and do not have GAP3 on their computers I have prepared an easy-to install gap3r4p4.zip file (9 megabytes) which contains just the two packages CHEVIE and VKCURVE and the necessary files of the GAP installation to run them; it also contains ready-made online help and manual in html formats) including the documentation for VKCURVE and CHEVIE. This .zip also contains ready-made Dos/Windows, Linux (for Intel) and Mac-OSX (for powerPC and Intel) executables. The installation instructions are as follows: unzip somewhere the file, it will make a gap3r4p4 directory. Then, in gap3r4p4/bin edit gap.sh (on Linux or Mac-OSX) or gap.bat (on dos/windows) so that the variable gap_dir refers to the right directory and executable, and put gap.sh (renamed gap) or gap.bat on someplace on your path. That is all, you are ready (remember to 'RequirePackage("chevie")' as explained above). In order to have a small .zip file, I have not included in this mini-distribution the list of small groups, 2-groups or 3-groups and most of the character tables from the Atlas or the tables of marks. I did not include either any package but VKCURVE and CHEVIE. You can add all these to your distribution by downloading the appropriate .zoo files from the GAP archives in St Andrews. I have also made a .dvi version of the manual (including the documentation for VKCURVE and CHEVIE; it is better than the html version for the display of the mathematics formulas). I have also made the .html GAP documentation available online.

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  Installing just the CHEVIE package

• First, download the tarred and gzipped(3.1M) or zipped(3.2M) gap source for CHEVIE.

  Then, you have two possibilities:

• You want to make the minimal effort to install the developement version of CHEVIE on your computer, or/and you want not to interfere with the GAP3 distribution on your machine. For this you will install the developement version of CHEVIE in a private place (like a subdirectory of your home directory). Attach to where you want to put CHEVIE and unpack the archive there. It will create a chevie directory at that place (so if you are John Smith and work on a UNIX system, and unpack in your home directory, the chevie directory will be at something like /users/smith/chevie). Then to call the developement version of chevie you have to execute the following instructions in gap (or add them to your .gaprc, which will cause CHEVIE to be loaded each time you start gap):

  PKGNAME:=Concatenation(["/users/smith/"],PKGNAME);
  RequirePackage("chevie");

• You have root access or you have your own PC or Macintosh, and you want to replace the distributed version with the developement version. Then attach to the directory where the CHEVIE package is in the distribution (something like /usr/local/lib/gap3r4p4/pkg/chevie; go to /usr/local/lib/gap3r4p4/pkg since the archive contains the relative path starting with the chevie part), and unpack the archive. Now, when you use the package by doing as usual

  RequirePackage("chevie");

  you will access the developement version (you can put this instruction in your .gaprc to not to have to repeat it every time).

  Only one thing will not have been updated: the CHEVIE chapters in the online (or not online, as well) GAP3 manual. The easiest way to update them is to copy the /doc subdirectory inside my pre-packaged archive gap3r4p4.zip to the GAP3 distribution.