The principal investigator will work on modular representation of finite groups of Lie type, and on the Macdonald symmetric functions and related functions. In modular representation theory she will investigate the Deligne-Lusztig operator and will try to obtain a combinatorial description in the case of the classical groups. She will also investigate the two-variable Green functions that appear in the context of the Macdonald symmetric functions in two variables. Finally she will investigate character values at a special class of orthogonal groups in odd dimension relating to random walks on classical 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.
