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

这项研究涉及到各种各样的问题 在无限维李的表示论中 代数 首席研究员将致力于模块化 不变表示，孤立子的例外族 方程，互反定律和无限维群， 分次单增长李超代数的分类 1，量子群。 许多不同的代数对象可以表示为 其他代数对象的变换的代数集合。 通过这些表示，它们的结构可以 测定 这个项目是关于 无穷维李代数理论 研究 这些代数在整个数学中都有应用， 数学物理

This research is concerned with a variety of problems in the representation theory of infinite dimensional Lie algebras. The principal investigator will work on modular invariant representations, exceptional hierarchies of soliton equations, reciprocity laws and infinite-dimensional groups, classification of graded simple Lie super-algebras of growth 1, and quantum groups. Many different algebraic objects can be represented as algebraic sets of transformations of other algebraic objects. Through these representations their structure can be determined. This project is concerned with the representation theory of infinite dimensional Lie algebras. The study of these algebras has applications throughout mathematics and mathematical physics.