Mathematical Sciences: Applications of the Representation Theory of Quantum Affine Lie Algebras to Solvable Lattice Models

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During the last two decades representation theory of affine Lie algebras has led to many interesting and important applications in many areas of mathematics and physics. One such connection has been established with certain two dimensional solvable lattice models in statistical mechanics. The interaction between quantum affine Lie algebras and solvable lattice models has recently led to many new discoveries both in representation theory of affine and quantum affine Lie algebras as well as solvable lattice models and integrable systems. Professor Miwa is a pioneer in this field and possesses a unique overview. He can give a well organized presentation of the major ideas and recent research results, and prescribe future directions for research in this field, during the course of the ten lectures. This project will support an NSF-CBMS Regional Research Conference in the Mathematical Sciences on Application of the Representation Theory of Quantum Affine Lie Algebras to Solvable Lattice Models, to be held June 1 - 5, 1993, on the main campus of North Carolina State University in Raleigh. Professor Tetsuji Miwa will be the principal lecturer/ To stimulate interest and activity in mathematical research, the National Science Foundation each year supports a number of NSF-CBMS Regional Research Conferences in the Mathematical Sciences. Each five-day conference features a distinguished lecturer who delivers ten lectures on a topic on important current research in one sharply focused area of the mathematical sciences. The lecturer subsequently prepares an expository monograph based upon these lectures, which is normally published by the American Mathematical Society or the Society for Industrial and Applied Mathematics, or jointly by the American Statistical Association and the Institute of Mathematical Statistics. Certain features differentiate these conferences from typical research conferences. These are: (1) Focus on a single important and timely area of research by a leading practitioner, (2) Continued effect and local stimulation through regional emphasis, (3) Panel review for quality, breadth, and timeliness, and (4) Published monographs for a wider audience.