Cohomology & Modular Representation Theory of Finite & Algebraic Groups

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9401292 Parshall This project is concerned with the modular representation theory of algebraic and associated finite groups. The principal investigators are interested in a solution of the famous conjecture of Lusztig for characters of the irreducible representations in characteristic larger than the Coxeter number. A successful solution to this problem would have many ramifications for finite groups. The work of the principal investigators has already established an important connection between the representation theory of algebraic groups and the theory of finite dimensional algebras. The principal investigators will also work on problems concerning finite groups, Lie algebras, and quantum groups. The research supported concerns the representation theory of finite groups. A group is an algebraic object used to study transformations. Because of this, groups are a fundamental tool in physics, chemistry and computer science as well as mathematics. Representation theory is an important method for determining the structure of groups.