REPRESENTATIONS OF SEMISIMPLE GROUPS OVER FIELDS OF POSITIVE CHARACTERISTIC
Abstract: The fundamental problem in the representation theory of semisimple groups in positive characteristic is to give a character formula for the irreducible finite dimensional representations and a decomposition formula for dual Weyl modules with multiplicities. All attempts at this problem have failed and no one seems to be thinking about it any longer. I will try to explain why this has come about beginning with the observation that we are using the wrong notion of weights and the wrong algebra over which the representations are supposedly modules. I will describe what I believe will be the ingredients of a meaningful character formula.
