Mathematical Sciences: Hypergeometric Series Very-Well- Poised on Semisimple Lie Algebras and Multivariate Orthogonal Polynomials

该奖项支持多变量超- 得克萨斯大学教授罗伯特·古斯塔夫森的几何级数 大学古斯塔夫森博士提出了一种理论， 在半单李上非常稳定超几何级数 代数，以及相应的理论β和梅林- 紧李群上的巴恩斯积分及相应的李群 代数此外，他计划将这一理论与 与根系相关的正交多项式族， 最近由麦克唐纳定义。 这项研究福尔斯属于广义的组合学范畴， 这是当今数学中最活跃的领域之一。 从根本上说，组合学代表了一个系统化的 首先是数学活动，计数在其 然而，现代的发展，组合学已经不仅仅是 计数利用各种先进的数学 技术，虽然它的根源可以追溯到几个世纪， 在过去的几十年里， 因为它在通信和信息方面的重要性， 技术.

This award supports the research on multivariable hyper- geometric series of Professor Robert Gustafson of Texas A & M University. Dr. Gustafson has proposed to develop the theory of hypergeometric series that are very well poised on semisimple Lie algebras, as well as the corresponding theory of beta and Mellin- Barnes integrals on compact Lie groups and the associated Lie algebras. In addition, he plans to relate this theory to the families of orthogonal polynomials associated to root systems, recently defined by Macdonald. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. Fundamentally, combinatorics represents a systematization of the very first of all mathematical activities, counting. In its modern development, however, combinatorics has gone beyond just counting to make use of a wide variety of advanced mathematical techniques, and although its roots go back several centuries, the field has had an explosive development in the past few decades because of its importance in communications and information technology.