arXiv subjects
Publications and source records attributed to Birte Johansson.
We verify the inductive McKay--Navarro condition for the groups $\mathsf{B}_2(2^f)$ and $\mathsf{G}_2(3^f)$ and all primes if $f$ is odd. Further, we show that the equivariance part of the inductive condition holds for all integers $f$.
The McKay--Navarro conjecture is a refinement of the McKay conjecture that additionally takes the action of some Galois automorphisms into account. We verify the inductive McKay--Navarro condition in the defining characteristic for the finite groups of Lie type with exceptional graph automorphisms, the Suzuki and Ree groups, $\mathsf{B}_n(2)$ ($n \geq 2$), and the groups of Lie type with non-generic Schur multiplier. This completes the verification of the inductive McKay--Navarro condition for the finite groups of Lie type in their defining characteristic.
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 $PSL_3(q)$ with $q \equiv 4,7$ mod $9$, $PSU_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.