Mathematical Sciences: Flag and Schubert Schemes - Classical, Generalized and Quantum

该项目涉及与Flag和Schubert方案相关的研究。主要研究工作如下：(1)建立Kac-Moody群的标准单项理论；(2)确定Schubert簇上奇点的重数；(3)建立Schubert簇上奇点上的切锥的标准单项理论；(4)确定了当w大于或等于t时的Kazhdan-Lusztig多项式P(w，t)；(5)写出了Schubert簇的正交丛的方程；(6)发展了有限和仿射情况下的量子Flag和Schubert格式理论。这个项目是关于代数群的研究。它结合了“纯”数学中最古老的三个领域：代数、分析和几何，但保形场理论的物理学家们对它非常感兴趣。

This project is concerned with research related to Flag and Schubert schemes. The principal investigator will work on the following problems: (1) develop a standard monomial theory for Kac-Moody groups; (2) determine the multiplicity of a singular point on a Schubert variety; (3) develop a standard monomial theory for tangent cones at singular points on a Schubert variety; (4) determine the Kazhdan-Lusztig polynomials P(w,t) for w greater than or equal to t; (5) write the equations of the conormal bundle of a Schubert variety; (6) develop a theory of quantum Flag and Schubert schemes in the finite and affine cases. This project is concerned with the study of algebraic groups. It combines three of the oldest areas of "pure" mathematics, algebra, analysis and geometry, yet it is of great interest to physicists working on conformal field theory.