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

DMS-9501290 PI：Varchenko 瓦尔琴科将发展理论的一般超几何理论与应用的代表性理论，共形场理论和统计力学。 特别是他将定义共形块WZW模型的共形场论作为一个特殊的空间的超几何函数，描述monodromy的共形块，解决量化Knizhnik-Zamolodchikov方程在q-超几何函数和描述代数结构的空间，其解决方案。 李群理论是以挪威数学家Sophus Lie的荣誉命名的，是世纪数学的重要课题之一。 李群表示论作为利用系统中固有对称性的数学工具，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。

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.