Mathematical Sciences: General Hypergeometric Functions in Representation Theory and Mathematical Physics

数学科学：表示论和数学物理中的一般超几何函数

• 批准号: 9501290
• 负责人: Alexander Varchenko
• 金额: $ 7.5万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-05-01 至 1998-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501290&HistoricalAwards=false
• 关键词: Mathematical; Sciences; General; Hypergeometric; Functions

DMS-9501290 PI: Varchenko Varchenko will develop the theory of general hypergeometric theory with applications to the representation theory, conformal field theory, and statistical mechanics. In particular he will define conformal blocks in WZW model of conformal field theory as a special space of hypergeometric functions, describe the monodromy of conformal blocks, solve the quantized Knizhnik-Zamolodchikov equation in q-hypergeometric functions and describe algebraic structures of the space of its solutions. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.

DMS-9501290 PI：Varchenko Varchenko 将发展一般超几何理论及其在表示论、共形场论和统计力学中的应用。 特别是，他将共形场论的WZW模型中的共形块定义为超几何函数的特殊空间，描述共形块的单调性，求解q-超几何函数中的量化Knizhnik-Zamoodchikov方程，并描述其空间的代数结构解决方案。 李群理论以挪威数学家索弗斯·李的名字命名，一直是二十世纪数学的主要主题之一。 作为利用系统固有对称性的数学工具，李群的表示论对数学本身（特别是分析和数论）以及理论物理学（特别是量子力学和基本粒子物理学）产生了深远的影响。