The Navarro refinement of the McKay conjecture for finite groups of Lie type in defining characteristic

Abstract

In this paper we verify Navarro's refinement of the McKay conjecture for quasi-simple groups of Lie type in their defining characteristic. Navarro's refinement takes into account the action of specific Galois automorphisms on the characters presents in the McKay conjecture [12]. Our proof of this case of the conjecture relies on a character correspondence constructed by Maslowski in [11]. Building on this we verify the inductive condition for Navarro's refinement from [14] for most groups of Lie type in defining characteristic.