This research is concerned with the Kazdhan-Lusztig theory. This involves Kac-Moody Lie algebras and groups, their representations and the combinatorics of Bruhat ordering on Coxeter groups. The principal investigator will study the combinatorics of Bruhat ordering, the geometry of Schubert varieties, and highest weight representations of Kac- Moody Lie algebras. This project is in the general area of Lie algebra. The principal investigator is concerned with the Kazhdan-Lusztig polynomials which are combinatorially defined objects having deep connections with structures in geometry and representation theory. This work is important in both mathematics and physics.
