# Darstellungstheorietage and Nikolaus Conference 2021

Speaker: Britta Späth (Wuppertal)

Title: Equivariant Jordan Decomposition

Abstract:

In the study of representations of finite reductive groups, Jordan decomposition of characters associates to each character in a rational Lusztig series a unipotent character of the centralizer of a semi-simple element in the dual group. The talk will focus on how and in which sense one can construct a Jordan decomposition of characters of $${\bf G}^F$$ which is equivariant with respect to Aut$$({\bf G}^F)$$ whenever $$\bf G$$ is a simple simply-connected algebraic group defined over a finite field through the Frobenius endomorphism $F$. The main difficulty comes from the disconnectedness of centralizers in the dual group $${\bf G}^*$$. This is part of the project to determine the action of Aut$$(G)$$ on Irr$$(G)$$ for all finite (quasi-)simple groups $$G$$.