Britta Späth

Towards the McKay Conjecture

During the last decade substantial progress in a final proof of the McKay conjecture has been made. I will give an overview of that development and its open questions. In those considerations a major concern is how group automorphisms act on characters of simple groups of Lie type. Using Jordan decomposition and Shintani descent the problem could be solved for symplectic groups by a counting argument. The last open cases are with simple groups of type D, where this problem becomes particular difficult since the outer automorphism group is bigger.