Super Duality and Deformations in the Representation Theory of Lie Superalgebras

在过去的四十年里，超对称一直是物理学和数学基础研究的中心阶段。目前，它正在日内瓦欧洲核子研究中心的大型强子对撞机上进行大规模实验。本项目旨在为解决超对称的基本问题创造新的数学概念和技术。预期的结果包括新型的玻色-费米对应，李超代数表示的变形理论，李超代数抛物型Verma模的Jantzen滤波的代数和几何处理，以及量子超群产生的结和3流形拓扑不变量的量子场论模型。

Supersymmetry has remained in a central stage of fundamental research in both physics and mathematics for the last forty years. It is currently being tested by experiments of massive scales conducted on the Large Hadron Collider at CERN in Geneva. The present project aims to create new mathematical concepts and techniques for addressing fundamental issues of supersymmetry. Expected outcomes include new types of Bose-Fermi correspondence, a deformation theory of Lie superalgebra representations, algebraic and geometric treatments of Jantzen filtration of parabolic Verma modules of Lie superalgebras, and quantum field theoretical models for the topological invariants of knots and 3-manifolds arising from quantum supergroups.