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We determine for all simple simply connected reductive linear algebraic groups defined over a finite field all irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank Ð our bound(More)
For the purposes of [K] and [KM] it became necessary to have 7 × 7 matrix generators for a Sylow-3-subgroup of the Ree groups 2 G 2 (q) and its normalizer. For example in [K] we wanted to show that in a seven dimensional representation the Jordan canonical form of any element of order nine is a single Jordan block of size 7. In [KM] we develop group(More)
If the subtitle ist not sufficient, this <TitleComment> element can be used for a slightly longer text on the front page. Abstract This document tries to use all elements that exist in GAPDoc. In addition, the final output not only contains the usual content, but also an appendix with the source text. There are also links from the usual content to the(More)
• contains library files holding information for finite complex reflection groups giving conjugacy classes, fake degrees, generic degrees, irreducible characters, representations of the groups and the associated Hecke algebras. The package is loaded using the command RequirePackage("chevie") (see 0.1). Compared to version 3, it is more general. For example,(More)
We report on the project of parallelising GAP, a system for computational algebra. Our design aims to make concurrency facilities available for GAP users, while preserving as much of the existing code base (about one million lines of code) with as few changes as possible and without requiring users---a large percentage of whom are domain experts in their(More)