Mathematical Sciences: The Combinatoric Structure of Representations of Semi-Simple Groups Over Valued Fields

数学科学：有价值域上半单群表示的组合结构

• 批准号: 9006321
• 负责人: William Haboush
• 金额: $ 3.46万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-04-01 至 1992-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9006321&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Combinatoric; Structure; Representations

This research is in the area of group representation theory. The principal investigator will develop an algebraic harmonic analysis to transfer the representation theory of semisimple groups to the representation theory of Hecke algebras. The central problem to be considered in this project is the Lusztig conjecture which states that certain invariants attached to an algebraic group can be calculated from polynomials. This is a difficult and central problem in group theory. It also has implications in other areas of mathematics.

本研究属于群体表征理论领域。 首席研究员将开发一个代数谐波 半单表示论的变换分析 Hecke代数的表示理论。 本项目要考虑的中心问题是 Lusztig猜想指出，某些不变量附加 可以从多项式中计算。 这 是群论中的一个难点和中心问题。 它也有 在其他数学领域的影响。