RESEARCH ON THE MODULAR REPRESENTATIONS OF FINITE GROUPS

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(1) Indecomposable modules over finite groupsSome contributions to the solution of the Broue conjecture are made especially in linear groups and the Glauberman correspondence cases. The tree classes of some Auslander-Reiten components for integral group rings of non cyclic p-groups are determined.(2) Endomorphism rings of permutation modulesThe orthgonality relation of characters of blocks of finite groups is generalized to that of blocks of Hecke algebras in the case where the base subgroup under consideration has order prime to the characteristic of the base field.Some new results are obtained about the number of irreducible modular constituents of Specht modules of the symmetric group.(3) Representation theory of groups of Lie typeSome foundations on the theory of D-modules in positive characteristic are established. A new approach is made using Kashiwara's crystal basis to Mathieu's theorem concerning the tensor products of modules with good filtrations.