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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)
• 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)
Acknowledgement We would like to thank the many people who have made contributions of various kinds to the development of GAP since 1986, in particular: The following list gives the authors, indicated by A, who designed the code in the first place as well as the current maintainers, indicated by M of the various modules of which GAP is composed. Since the(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)