Mathematical Sciences: Algebraic Groups - Combinatorial, Geometric and Representation - Theoretic Aspects

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This award supports work related to the combinatorial, geometric and representation-theoretic aspects of semi-simple algebra groups. In particular, the principal investigator will determine the singular loci of Schubert varieties; will determine the multiplicity of a singular point on a Schubert variety; will establish Postulation formulae for tangent cones at singular points on a Schubert variety; and will write the equations of the conormal bundle of a Schubert variety. She will also develop a Standard Monomial Theory for Quivers; and will devise a combinatorial construction for quantum groups. The research supported involves invariant theory and algebraic groups. In general, invariant theory involves the actions of linear algebraic groups on manifolds or linear spaces and the determination of the mathematical invariants of the space under these group actions.