## The MAPLE-part of CHEVIE

This part of CHEVIE deals with generic character tables of series of groups of Lie type. An example of such a series is the set of groups $GL$3(q), where $q$ runs through all prime powers. For other examples see the list of available tables below.

Here is an outline of the content of this part of CHEVIE. It includes

• a library of known ordinary generic character tables of series of finite groups of Lie type
• a library of Green functions of such groups
• programs for printing (parts of) these tables on screen or in LaTeX format
• programs for printing information on conjugacy classes, characters or references to the literature
• programs for computing with these tables: orthogonality relations, structure constants, tensor product (without specializing the $q$)
At the moment we distribute generic character tables for the following series of groups.
• $SL$2(q), $PGL$2(q), $GL$2(q), $PSL$2(q), $GU$2(q)
• $SL$3(q), $PGL$3(q), $GL$3(q), $PSL$3(q) and corresponding unitary groups
• $Sp$4(q) ($q$ even), $CSp$4(q) ($q$ odd)
• $G$2(q)
• Suzuki groups $2B$2(q) ($q2=22k+1$)
• Ree groups $2G$2(q) ($q2=32k+1$)
• $Sp$6(q) ($q$ even), $CSp$6(q) ($q$ odd)
• Steinberg groups $3D$4(q)
• Ree groups $2F$4(q) ($q2=22k+1$)
• tables of unipotent characters: $D$4(q), $2D$4(q), $GL$n(q) ($n < 9$)
• complete tables for $GL$n(q) and $GU$n(q), n = 4, 5, 6, are available in an extra archive

For more information on the programs in this part of CHEVIE you can study the manual (in gzipped dvi format (39k) or in gzipped postscript format (90k)).

Remarks on new releases: The programs in this package need (and work well with) Maple-V.3, which is quite old now. We have only added some tables later on. The reason is that Maple changes substantial feature of their system in new releases. For example in Maple-V.4 the online help of our package does no longer work (but the programs do, as far as I know). In Maple-V.5 even the programming language has changed such that our programs are no longer valid Maple code. We are not willing to spend a lot of time on updating the package because of such changes of the base system. There is a project to transfer this part of CHEVIE into a GAP package, but that is not so easy.

VERSION for Maple 7 and newer: Johannes Maslowski kindly provided a translation of the package to Maple 7 and newer versions.