Abstract Peter Fiebig

Recent developments around Lusztig's conjecture

Abstract: Lusztig stated in 1981 a formula for the simple rational characters of reductive algebraic groups defined over a field of positive characteristic p. In the case of GL_n(k) it was expected that the formula holds for p>n. In 1990 it was shown in a combined effort of several authors that the conjecture is true if the characteristic is ``big enough''. In 2007 a first upper bound on the exceptions was found, which, however, is an enormously huge number. Very recently, Geordie Williamson found a series of counterexamples with p>n, which came as a big surprise for representation theorist. I will report on these events and maybe speculate about what we can expect to be a plausible answer now.