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

数学科学：量子仿射李代数表示论在可解格子模型中的应用

• 批准号: 9215075
• 负责人: Kailash Misra
• 金额: $ 2.3万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-01-01 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9215075&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Applications; Representation; Theory

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.

在过去的二十年里，仿射表示理论 李代数已经导致了许多有趣和重要的 在数学和物理学的许多领域的应用。 一个这样 已经建立了与某些二维 统计力学中的可解晶格模型 的 量子仿射李代数与可解李代数相互作用 晶格模型最近导致了许多新的发现， 仿射和量子仿射李代数的表示理论 以及可解晶格模型和可积系统。 Miwa教授是该领域的先驱，拥有独特的 概况. 他能很好地组织这个专业的介绍 思想和最近的研究成果，并规定未来 在这一领域的研究方向，在整个过程中， 十堂课。 该项目将支持NSF-CBMS区域研究 数学科学应用会议 可解量子仿射李代数的表示理论 格模型，将于1993年6月1日至5日在主校区举行 位于罗利的北卡罗来纳州州立大学的教授。 哲二教授 Miwa将担任首席讲师/为了激发兴趣， 数学研究活动，国家科学 基金会每年支持一些国家科学基金会-CBMS区域 数学科学研究会议。 每五天 会议设有一个杰出的讲师谁提供十 关于当前重要研究主题的讲座， 数学科学的重点领域。 讲师 随后根据这些内容编写了一本简明的专著。 演讲，通常由美国人出版， 数学学会或工业与应用数学学会 数学，或由美国统计协会联合 和数理统计研究所。 某些特征 将这些会议与典型的研究区分开来 两会 （1）注重一个重要的、 由一位领先的从业者进行及时的研究领域，（2）续 通过区域重点的影响和当地刺激，（3） 小组审查质量、广度和及时性，以及（4） 为更广泛的读者出版专著。