A5: Decomposition matrices

The main aim of the project is the determination of the l-modular decomposition matrices of blocks of finite exceptional groups of Lie type in non-defining good characteristic for large primes l. The methods are of a theoretical as well as computational nature, and include Harish-Chandra theory, Gelfand-Graev characters, and projective modules in intersection cohomology groups. The results shall be applied to verify instances of famous open conjectures in modular representation theory, in particular Navarro’s Galois-McKay conjecture. The decomposition matrices shall be made publically available in electronic form.