Inductive McKay Condition in defining Characteristic

TL;DR

This paper reformulates the inductive McKay condition and proves it for simple groups of Lie type in their defining characteristic, extending previous results and utilizing recent advances in the field.

Contribution

It introduces a new formulation of the inductive McKay condition and applies it to simple groups of Lie type in characteristic p, confirming the condition in these cases.

Findings

Simple groups of Lie type satisfy the inductive McKay condition for their defining prime p.

The new criterion reestablishes earlier results for non simply-laced and non-classical types.

Utilizes recent results by Maslowski to achieve these proofs.

Abstract

We reformulate the inductive McKay condition, from Isaacs-Malle-Navarro, and apply the new criterion to simple groups of Lie type, when the prime is the defining characteristic p. Thereby we make use of a recent result of Maslowski. This proves that these simple group satisfy the inductive McKay condition for p. In the non simply-laced types and non-classical types this reproves earlier results by Brunat and Brunat-Himstedt.