On the inductive McKay–Navarro condition for finite groups of Lie type in their defining characteristic

Abstract

The McKay–Navarro conjecture is a refinement of the McKay conjecture that additionally takes the action of some Galois automorphisms into account. We verify the inductive McKay–Navarro condition in the defining characteristic for the finite groups of Lie type with exceptional graph automorphisms, the Suzuki and Ree groups, Bn(2) (n≥2), and the groups of Lie type with non-generic Schur multiplier. This completes the verification of the inductive McKay–Navarro condition for the finite groups of Lie type in their defining characteristic.