This project is concerned with the Kazhdan-Lusztig conjecture in the modular representation theory of semisimple algebraic groups. The principal investigators will make use of quasi-hereditary algebras and highest weight categories in attacking this problem. Questions involving representations of finite groups and Lie algebras will also be considered. The central problem to be considered in this project is the Kazhdan-Lusztig conjecture which states that certain invariants attached to an algebraic group can be calculated from polynomials. This is a difficult and central problem in group theory. It also has implications in other areas of mathematics.
