ALGB Seminar: Niamh Farrell (TU Kaiserslautern, Germany)

12/03/2019 - 16:00

Title: Fake Galois actions

Abstract: Let $G$ be a finite group of order $n$. The Galois group Gal$(\mathbb{Q}_n / \mathbb{Q})$ permutes the set of ordinary irreducible characters of $G$ but has, in general, no natural action on the set of Brauer characters of $G$. I will introduce the concept of fake Galois actions, as defined by Sp\"ath and Vallejo Rodr\'iguez. I will show the existence of fake Galois actions for the Brauer characters of finite simple groups, and discuss the connection between this result and a modular analogue of the Glauberman Isaacs correspondence. This is joint work with Lucas Ruhstorfer.