Frank Luebeck (Aachen Unversity)
Computing characters and representations
of finite groups of Lie type in their defining characteristic
The representations in question are parameterized in terms
of \emph{highest weights} and are closely related to rational
representations of reductive algebraic groups and their Lie algebras.
The degrees of the representations are generally not known
(but in some cases there exists a conjecture by Lusztig).
An overview on this background will be given, as
well as some results and applications.
In this talk \emph{computing} means a practical computing of explicit
characters and representing matrices using a computer.