Mathematical Sciences: Representation Theory of Infinite Dimensional Lie Algebras and Applications

这个项目涉及到的各种问题， 无限维李代数的面积校长 研究人员将研究与以下因素相关的无限维组： 卡茨-穆迪代数，Virasoro代数的表示， 孤立子方程的例外族，超可积的 系统和模空间。 根据该奖项进行的研究涉及 无限空间的拓扑和代数几何结构 Kac-Moody代数上的维数群及其标志 品种对这些Kac-Moody代数的研究 应用于数学和数学物理。

This project is concerned with a variety of problems in the area of infinite dimensional Lie algebras. The principal investigator will study infinite-dimensional groups associated to Kac-Moody algebras, representations of the Virasoro algebra, exceptional hierarchies of soliton equations, superintegrable systems, and moduli spaces. The research conducted under this award concerns the topological and algebra-geometric structure of infinite dimensional groups attached to Kac-Moody algebras and their flag varieties. The study of these Kac-Moody algebras have applications throughout mathematics and mathematical physics.