Mathematical Sciences: Representations of Affine Lie Algebras and Quantum Groups and Conformal Field Theory

数学科学：仿射李代数和量子群的表示以及共形场论

• 批准号: 9401215
• 负责人: Feodor Malikov
• 金额: $ 7.07万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401215&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representations; Affine; Lie

9401215 Malikov This award supports research on the representation theory of affine Lie algebras and quantum groups. The principal investigator will work on (1) affine Lie algebra modules realized in multi-valued functions on a flag manifold; (2) Wess-Zumino-Witten model at a critical level; (3) complex powers in algebra and geometry; and (4) the Gel'fand-Kirillov conjecture for quantum groups. Many different algebraic objects can be represented as algebraic sets of transformations of other algebraic objects. Through these representations their structure can be determined. This project is concerned with the representation theory of infinite dimensional Lie algebras. The study of these algebras has applications throughout mathematics and mathematical physics. ***

9401215 Malikov 该奖项支持仿射李代数和量子群的表示理论的研究。 主要研究者将致力于（1）在旗流形上实现多值函数的仿射李代数模块;（2）临界水平的Wess-Zumino-维滕模型;（3）代数和几何中的复幂;以及（4）量子群的Gel'fand-Kirillov猜想。许多不同的代数对象可以表示为其他代数对象的变换的代数集合。 通过这些表征，可以确定它们的结构。 这个项目是关于无限维李代数的表示理论。 对这些代数的研究在整个数学和数学物理中都有应用。 ***