Decomposition matrices for exceptional groups of Lie type


The aim of this project is the determination of ℓ-modular decomposition matrices for blocks of exceptional groups of Lie type with defect groups of rank 2. The methods will be partly theoretical, partly computational, utilizing among other ingredients Harish-Chandra induction and Hecke algebras, generalised Gelfand-Graev representations, tensor products, and projective modules coming from intersection cohomology. The results will be used to verify open conjectures in representation theory for the blocks considered. They will be made available in electronic form through a database.