Mathematical Sciences: Inner Ideal Geometries and AssociatedGroups in Representations of Affine Lie Algebras

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Let M be an irreducible highest weight representation of an affine Lie algebra. This project is concerned with the inner ideal geometry in M and the associated group G. The principal investigator will study the algebraic and topological structure of M. She will also work on a characterization of the Kac-Moody group associated with the affine Lie algebra in terms of inner ideal geometries. An explicit description of the inner ideal geometry associated with M will be derived. The research supported falls in the general area of geometric algebra which is concerned with vector spaces, coordinatization, and the transformation groups acting on the spaces. Questions concern both the underlying geometry and the algebra.