Jay Taylor — 2018

Automorphisms and Characters of Finite Groups

Abstract: The complex irreducible characters of a finite group G are of central importance to the representation theory of finite groups. The automorphism group of a finite group, as well as certain Galois automorphisms, acts on its sets of irreducible characters. In general it is a difficult problem to describe these actions. In this work we present results concerning the action of the automorphism group on the irreducible characters of the finite symplectic groups Sp(2n,q), where q is an odd prime power. We also present joint work with Schaeffer–Fry establishing a conjecture of Navarro which relates the property of having a self-normalising Sylow 2-subgroup to the action of certain Galois automorphisms on the irreducible characters.