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

该奖项支持美国德州农工大学罗伯特·古斯塔夫森教授关于多变量超几何级数的研究。Gustafson博士提出发展半简单李代数上的超几何级数理论，以及紧李群和相关李代数上的β积分和Mellin- Barnes积分的相应理论。此外，他计划将这一理论与麦克唐纳最近定义的与根系相关的正交多项式族联系起来。这项研究属于组合学的广泛范畴，这是当今数学中最活跃的领域之一。从根本上说，组合学代表了对所有数学活动——计数——的系统化。然而，在其现代发展中，组合学已经不仅仅是计算，而是利用了各种各样的先进数学技术。尽管它的根源可以追溯到几个世纪以前，但由于它在通信和信息技术中的重要性，该领域在过去的几十年里有了爆炸性的发展。

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.