The principal investigator will work on the representation theory of reductive algebraic groups and related finite and infinitesimal groups. The particular topics to be investigated are: constructions for the reduction mod p of irreducible complex representations of the finite groups; determination of the Loewy series of principal indecomposable modules for finite groups of Lie type; support varieties of Weyl modules and simple modules; the adjoint representation on the regular functions on nilpotent orbits and their closures. A group is an algebraic structure with a multiplication defined on it. Finite groups may be viewed as algebraic sets of transformations of vector spaces. Their properties and structure can be determined through these representations.
