### A counterexample to a conjecture of Steinberg

Algebra and Geometry Seminar

15th May 2019, 2:30 pm – 3:30 pm

Howard House, 4th Floor Seminar Room

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.

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