Mathematical Sciences: Cohomology and Modular Representations of Algebraic Groups

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This research is concerned with the representation theory of algebraic groups. The principal investigator will study the structure of the indecomposable rational injective modules for certain non-reduced subgroup schemes of a simply connected semisimple algebraic group. In addition, the structure of the Jantzen translations of these injective modules and the relationship between this structure and the Hecke algebra of the affine Weyl group will be studied. This project is concerned with the structure, cohomology and representations of algebraic groups. These algebraic groups occur, for example, as groups of linear transformations. This is an active area currently in mathematics. This project will provide a key step in solving the Lusztig conjecture in characteristic p.