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

Birte Johansson

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

Representation Theory 2022-02-03 v2

Authors: Birte Johansson

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 $PSL_3(q)$ 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.

Keywords

inductive mckay-navarro condition suzuki groups ree groups galois-equivariant jordan decomposition irreducible characters psl3 psu3 g2

Cite

@article{arxiv.2110.10946,
  title  = {The inductive McKay--Navarro condition for the Suzuki and Ree groups},
  author = {Birte Johansson},
  journal= {arXiv preprint arXiv:2110.10946},
  year   = {2022}
}

Comments

v2: some minor corrections, closed a gap in the proof of (new) Prop. 4.3

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

Abstract

Keywords

Cite

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