Representation Theory of Infinite-Dimensional Lie Algebras and Applications

无限维李代数表示论及其应用

• 批准号: 9622870
• 负责人: Victor Kac
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622870&HistoricalAwards=false
• 关键词: Representation; Theory; Infinite; Dimensional; Lie

9622870 Kac This grant supports the research of Professor V. Kac to work on various problems in representation theory and mathematical physics. He will study the representation theory of the Lie algebra of differential operators on the circle as well vertex operators, quantum groups and conformal quantum field theory. He will also study soliton equations, integral representations of affine superalgebras and the relationship between reciprocity laws in number theory and the representation theory of infinite dimensional 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 thought 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.

小行星9622870 该补助金支持V. Kac教授的研究，以解决表示论和数学物理中的各种问题。他将研究代表理论的李代数微分算子的圆以及顶点运营商，量子群和共形量子场论。他还将研究孤子方程，仿射超代数的积分表示和相互关系的法律在数论和代表理论的无限维群体。 这是一项从代数领域开始的研究，但超越了代数领域，涉及数论和理论物理。 这些联系的原因是，代数可以被认为是对抽象对称性的研究。因此，代数直接应用于物理和化学领域。特别是现代物理学中的规范场理论广泛地使用了这一领域的代数，本项目将详细研究其中的一些联系。还有编码理论和跨通信线路的数据传输。