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

数学科学：半简单李代数和多元正交多项式上的超几何级数非常平衡

• 批准号: 9002342
• 负责人: Robert Gustafson
• 金额: $ 3.66万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002342&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Hypergeometric; Series; Very

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.

该奖项支持德克萨斯农工大学Robert Gustafson教授的多变量超几何级数研究。 Gustafson 博士提议发展超几何级数理论，该理论非常适合半简单李代数，以及紧致李群和相关李代数上的相应 beta 和 Mellin-Barnes 积分理论。此外，他计划将该理论与麦克唐纳最近定义的与根系统相关的正交多项式族联系起来。 这项研究属于组合数学的广泛范畴，组合数学是当今数学中最活跃的领域之一。 从根本上说，组合学代表了所有数学活动中最重要的活动——计数的系统化。然而，在其现代发展中，组合数学已经超越了仅仅计数，而是利用了各种先进的数学技术，尽管其根源可以追溯到几个世纪前，但由于其重要性，该领域在过去几十年中得到了爆炸性的发展在通信和信息技术领域。