Mathematical Sciences: Solvable Lattice Models in Statistical Mechanics

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This research program will explore the connections between exactly solvable lattice models in lattice statistical mechanics and the representation theory of Kac-Moody Lie algebras. The long term goal is to connect the present understanding of exactly solvable models with that of the representation theory of certain Kac-Moody Lie algebra. The immediate task will be the study of specific solvable models and their relations to loop groups. Successful accomplishment of the immediate research project will enhance the methodology for solvable models in the statistical mechanics aspects of physics. This in turn will lead to a better understanding, utilization and control of materials and matters in technical applications as well as in our daily life.