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.

这项研究属于群表示理论领域。 首席研究员将开发代数调和分析，将半单群的表示论转移到赫克代数的表示论。 该项目要考虑的核心问题是 Lusztig 猜想，该猜想指出代数群的某些不变量可以通过多项式计算。 这是群论中的一个难题和核心问题。 它对数学的其他领域也有影响。