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

本研究涉及无限维李代数的表示理论中的各种问题。首席研究员将研究模不变表示、孤子方程的例外层次、互易定律和无限维群、增长1的分级简单李超代数的分类和量子群。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。通过这些表示可以确定它们的结构。本课题研究无限维李代数的表示理论。这些代数的研究在整个数学和数学物理中都有应用。

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.