This research is concerned with shape algebras of reductive algebraic groups. The principal investigator will consider their q-deformation and tensor operators on the flag manifolds. Roughly speaking, an algebraic group is a group which satisfies a polynomial. These groups have become increasingly important in mathematics and physics. Shape algebras provide a model of these algebraic groups. The aim of this research is to verify properties of the simpler shape algebra and then show that they translate to properties of the algebraic group.
