Mathematical Sciences: Quantum Kac-Moody Groups and RelatedQuestions

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9623327 Soibelman This grant supports the research of Professor Y. Soibelman to work on various problems in the theory of Kac-Moody groups. In particular he will study problems arising from the tensor structures in the theory of quantum affine algebras and compound versions of Lie bialgebras. He then will apply these results to quantum tau functions and quantum Weyl functions. Finally, he wishes to study chiral problems in the theory of quantum groups. This is research that starts out in the field of algebra but moves beyond that to touch both number theory and theoretical physics. The reasons for these connections are that algebra can be though of as the study of symmetry in the abstract. As such algebra has direct applications to areas of physics and chemistry. In particular the modern theory of gauge fields in physics uses this area of algebra extensively and this project will study some of these connections at length. There are also connections to coding theory and the transmission of data across communication lines.