Representations of Groups of Lie Type

Abstract

The final chapter is the representation theory of groups of Lie type, both in defining and non-defining characteristics. The first section deals with defining characteristic representations, introducing highest weight modules, Weyl modules, and building up to the Lusztig conjecture, with a diversion into Ext1 between simple modules for the algebraic group and the finite group. After that we switch to characteristic 0, discussing unipotent characters, their construction and properties. The third section considers positive characteristic, assigning the unipotent characters to blocks and discussing the various conjectures about their structure. The final section considers the blocks that are not unipotent, centring around the Bonnafe–Rouquier theorem that links arbitrary blocks to isolated blocks, a generalization of unipotent blocks.