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

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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.