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

DMS-9501290 PI：Varchenko Varchenko将发展一般超几何理论的理论，并将其应用于表象理论、保形场理论和统计力学。特别地，他在保形场论的WZW模型中将保形块定义为一种特殊的超几何函数空间，描述保形块的单行性，在q-超几何函数中求解量子化的Knizhnik-Zamolodchikov方程，并描述其解空间的代数结构。李群理论是以挪威数学家索菲斯·李的名字命名的，一直是20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，李群的表示理论对数学本身，特别是在分析和数论方面，以及对理论物理，特别是量子力学和基本粒子物理，都产生了深远的影响。

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.