The inductive McKay–Navarro condition for the Suzuki and Ree groups and for groups with non-generic Sylow normalizers

Abstract

We verify the inductive McKay–Navarro condition for the Suzuki and Ree groups for all primes as well as for ℓ=3 and the groups PSL3(q) with q≡4,7mod9, PSU3(q) with q≡2,5mod9, and G2(q) with q≡2,4,5,7mod9. On the way, we show that there exists a Galois-equivariant Jordan decomposition for the irreducible characters of the Suzuki and Ree groups.