The inductive McKay--Navarro condition for the Suzuki and Ree groups

Abstract

We verify the inductive McKay--Navarro condition for the Suzuki and Ree groups for all primes as well as for $p=3$ and the groups $PS{L}_3(q)$ with $q\equiv 4,7$ mod $9$, $PS{U}_3(q)$ with $q\equiv 2,5$ mod $9$, and $G_2(q)$ with $q=2,4,5,7$ mod $9$. On the way, we show that there exists a Galois-equivariant Jordan decomposition for the irreducible characters of the Suzuki and Ree groups.

arXiv commentv2: some minor corrections, closed a gap in the proof of (new) Prop. 4.3