On the unitriangularity of decomposition matrices of finite groups of Lie type of exceptional type

Abstract: Decomposition matrices encode the link between ordinary and modular representations of finite groups. In 2020, Brunat--Dudas--Taylor showed that the decomposition matrix of the unipotent $\ell$-blocks of a finite group $G$ of Lie type in good characteristic has unitriangular shape, answering a conjecture of Geck. Their theorem holds under some conditions on the prime $\ell$, in particular when $\ell$ is good. In this talk, we will discuss how to extend this result, firstly to $\ell$ bad (for any $G$ simple adjoint) and then to other blocks, namely the isolated blocks (for $G$ simple adjoint of type $G_2$, $F_4$, and $E_6$). This work was part of my PhD thesis under the supervision of Gunter Malle and Olivier Dudas.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.