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，并将其应用于表示理论、共形场理论和统计力学。特别是将共形场论的WZW模型中的共形块定义为一个特殊的超几何函数空间，描述共形块的单一性，求解q-超几何函数中的量子化Knizhnik-Zamolodchikov方程，并描述其解的空间的代数结构。李群理论是为了纪念挪威数学家索夫斯·李而命名的，它一直是20世纪数学的主要主题之一。作为利用系统中固有对称性的数学工具，李群表示理论对数学本身，特别是分析和数论，以及理论物理，特别是量子力学和基本粒子物理产生了深远的影响。

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.