This award supports research on the theory of Lie algebras. The principal investigator will work on proving a general Kazhdan-Lusztig conjecture for some rings associated to reflection representations of Coxeter groups. It is expected that, for crystallographic Coxeter groups, study of these rings and their integral forms will have important consequences for some central problems in Lie theory. The main object of the research is to obtain additional information on the structure of these rings and related algebras. This project is concerned with the study of Lie algebras and , in particular, with the Kahzdan-Lusztig polynomials. The Kahzdan-Lusztig polynomial is a combinatorially defined object having deep connections with structures in geometry and representation theory. This work is important both in mathematics and physics.
