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

TL;DR

This paper verifies the inductive McKay--Navarro condition for various finite groups of Lie type in their defining characteristic, including exceptional automorphisms, Suzuki, Ree, and certain groups with non-generic Schur multipliers.

Contribution

It completes the verification of the inductive McKay--Navarro condition for all finite groups of Lie type in their defining characteristic.

Findings

Verification for groups with exceptional automorphisms

Verification for Suzuki and Ree groups

Verification for groups with non-generic Schur multipliers

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, $\mathsf{B}_n(2)$ ($n \geq 2$), 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.