Résume | Abstract : In this talk we consider connected reductive groups over algebraically closed fields and corresponding finite groups of Lie type. We are interested in their irreducible representations over fields of their defining characteristic. A parameterization of these representations in terms of highest weights is well known. But in general the charaters of these representations or even their degrees are not known. If the characteristic is ``big enough'' (this depends on the type of the group) there is a famous conjecture by Lusztig that together with some more theory would yield the characters. This conjecture is known to be true in certain cases. If the characteristic is not ``big enough'' nothing general is known. In my talk I will give a survey of this background, and then concentrate on the question of which of these characters and representations can be determined by explicit computations. |