Frank Lübeck

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CHEVIE is a computer algebra package which collects data and programs for the representation theory of finite groups of Lie type and associated structures. We explain the theoretical and conceptual background of the various parts of CHEVIE and we show the usage of the system by means of explicit examples. More precisely, we have sections on Weyl groups and(More)
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 l our bound(More)
The εi are called the elementary divisors of A and à is called the Smith normal form or elementary divisors form of A. In Section 3 we give an algorithm for computing for a given matrix A, its rank r and a prime p the p-parts of the elementary divisors of A. During the algorithm we perform row operations on the matrix A which are driven by only considering(More)
Last but not least bedanke ich mich bei meinen Eltern, die mir — neben vielem Anderen — die Ausbildung ermöglicht haben, ohne die ich die vorliegende Arbeit nicht hätte erstellen können. 1, n)} die Menge der Nachbartranspositionen in S n. Dann lässt sich jedes Element von S n als Produkt von Elementen von S schreiben. Die Iwahori-Hecke-Algebra H A (u) zur(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)
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 G2(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 recognition(More)
We derive a Murnaghan–Nakayama type formula for the values of unipotent characters of finite classical groups on regular semisimple elements. This relies on Asai’s explicit decomposition of Lusztig restriction. We use our formula to show that most complex irreducible characters vanish on some -singular element for certain primes . As an application we(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)