Mathematical Sciences: Representations of Affine Lie Algebras and Quantum Groups and Conformal Field Theory

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9401215 Malikov This award supports research on the representation theory of affine Lie algebras and quantum groups. The principal investigator will work on (1) affine Lie algebra modules realized in multi-valued functions on a flag manifold; (2) Wess-Zumino-Witten model at a critical level; (3) complex powers in algebra and geometry; and (4) the Gel'fand-Kirillov conjecture for 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. ***