Abstract:

Let G be a semisimple algebraic group over an algebraically closed field K. At the 1966 ICM in Moscow, Robert Steinberg conjectured that two elements of G are conjugate if and only if their images are conjugate under every rational irreducible representation of G. The conjecture was proven by Steinberg in the case where K has characteristic zero, and also in the case where the two elements are semisimple. In this talk, I will present a counterexample which was discovered by computational methods.