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

该奖项支持与半简单代数群的组合、几何和表示理论方面有关的工作。特别是，首席研究员将确定舒伯特品种的单一位点；将决定舒伯特变换上奇点的多重性；建立舒伯特变元上奇点处切锥的公设公式；写出舒伯特变换的法向束的方程。她还将发展一个标准单项式理论；并将为量子群设计一种组合结构。支持的研究涉及不变量理论和代数群。一般来说，不变量理论涉及线性代数群在流形或线性空间上的作用，以及在这些群作用下空间的数学不变量的确定。

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.