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

## TL;DR

This paper confirms Navarro's refined version of the McKay conjecture for certain finite groups of Lie type in their defining characteristic, using character correspondences and Galois automorphisms.

## Contribution

It provides the first verification of Navarro's refinement for these groups, extending the understanding of the McKay conjecture in this context.

## Key findings

- Verified Navarro's refinement for most groups of Lie type in defining characteristic.
- Established a character correspondence based on Maslowski's work.
- Verified the inductive condition for Navarro's refinement in these cases.

## 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 present in the McKay conjecture. Our proof of this case of the conjecture relies on a character correspondence constructed by Maslowski. Building on this we verify the inductive condition for Navarro's refinement for most groups of Lie type in defining characteristic.