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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)

We describe a new implementation of direct condensation, which is a tool in computational representation theory. The crucial point for this is the enumeration of very large orbits for a group acting on some set. We present a variation of the standard orbit enumeration algorithm that reduces the amount of storage needed and behaves well under… (More)

We describe a " semi-modular " algorithm which computes for a given integer matrix A of known rank and a given prime p the multiplicities of p in the factorizations of the elementary divisors of A. Here " semi-modular " means that we apply operations to the integer matrix A but the operations are driven by considering only reductions of row vectors modulo… (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)

- Frank Lübeck
- 2007

- Frank Lübeck
- 2006

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)