Dade's Invariant Conjecture for the Ree groups 2F4(q^2) in Defining Characteristic

TL;DR

This paper proves Dade's invariant conjecture for the simple Ree groups 2F4(2^{2n+1}) in characteristic 2, confirming the conjecture for these groups and completing the proof for all such Ree groups.

Contribution

It provides a complete proof of Dade's invariant conjecture for the simple Ree groups 2F4(2^{2n+1}) in the defining characteristic.

Findings

Dade's conjecture verified for all Ree groups 2F4(2^{2n+1}) in characteristic 2

Completes the proof of Dade's conjecture for these Ree groups

Advances understanding of representation theory of Ree groups

Abstract

We verify Dade's invariant conjecture for the simple Ree groups 2F4(2^{2n+1}) for all n > 0 in the defining characteristic, i.e., in characteristic 2. This completes the proof of Dade's conjecture for the simple Ree groups 2F4(2^{2n+1}).