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

在过去的二十年里，仿射李代数的表示理论在数学和物理的许多领域产生了许多有趣和重要的应用。一种这样的联系已经与统计力学中的某些二维可解晶格模型建立。近年来，量子仿射李代数与可解格模型的相互作用在仿射和量子仿射李代数的表示理论以及可解格模型和可积系统等方面都产生了许多新的发现。Miwa教授是这一领域的先驱，具有独特的观点。在十场讲座的过程中，他可以很好地组织地介绍主要思想和最近的研究成果，并规定该领域未来的研究方向。该项目将支持将量子仿射李代数的表示理论应用于可解格子模型的NSF-CBMS数学科学区域研究会议，会议将于1993年6月1日至5日在罗利的北卡罗来纳州立大学主校园举行。Tetsuji Miwa教授将担任首席讲师/为了激发人们对数学研究的兴趣和活动，国家科学基金会每年支持一些NSF-CBMS数学科学区域研究会议。每个为期五天的会议都有一位杰出的讲师，他就一个重要的当前研究主题发表了十次演讲，该主题是数学科学中一个尖锐的重点领域。讲师随后根据这些讲座编写一份说明性专著，通常由美国数学学会或工业和应用数学学会出版，或由美国统计协会和数学统计研究所联合出版。这些会议的某些特点使其有别于典型的研究会议。它们是：(1)由领先的实践者专注于一个重要和及时的研究领域，(2)通过区域重点来持续影响和局部刺激，(3)小组审查质量、广度和及时性，以及(4)出版面向更广泛受众的专著。

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.