The focus of this research is on the representations of Lie algebras, Lie groups, and quantum groups, and their combinatorics. The principal investigator will work on (1) centralizer algebras of tensor representations; (2) Weyl group symmetric functions; (3) branching rules and centralizer algebras; and (4) weight and root multiplicities for Kac-Moody Lie algebras. This research is concerned with a mathematical object called a Lie algebra. Lie algebras arise from another object called a Lie group. An example of a Lie group is the rotations of a sphere where one rotation is followed by another. Lie groups and Lie algebras are important in areas involving analysis of spherical motion.
