Root Systems and Special Functions

根系统和特殊功能

• 批准号: 0070814
• 负责人: Siddhartha Sahi
• 金额: $ 6万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-06-15 至 2004-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070814&HistoricalAwards=false
• 关键词: Root; Systems; Special; Functions

The proposal is in the area of the theory of hypergeometricfunctions associated to root systems, and their q-deformations.A number of key results have been obtained by the investigatorin the course of previous NSF supported research. These resultshave led to the resolution of various conjectures of Dunkl,Macdonald, Koornwinder and others. It is proposed to examinesome of the outstanding problems in this area, which have todo with certain positivity conjectures of Macdonald, Stanley, and theproposer.The research described above should lead to a better understandingof several different areas of mathematics including algebra, representation theory, combinatorics, analysis, and multivariate statistics.

这个建议是在与根系相关的超几何函数理论领域，以及它们的q-变形。研究者在以往NSF资助的研究过程中获得了许多关键成果。这些结果解决了Dunkl、Macdonald、Koornwinder等人的各种猜想。本文建议对这一领域的一些突出问题进行研究，这些问题与麦克唐纳、斯坦利和提出者的某些积极猜想有关。以上所述的研究将有助于更好地理解数学的几个不同领域，包括代数、表示理论、组合学、分析和多元统计。