Mathematical Sciences: Representations of Affine Hecke Algebras and Quantum Groups

数学科学：仿射赫克代数和量子群的表示

• 批准号: 9500016
• 负责人: George Lusztig
• 金额: $ 27.86万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500016&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representations; Affine; Hecke

This award supports research on the representation theory of affine Hecke algebras and quantum groups. The principal investigator will work on completing the classification of the unramified representations of semisimple split p-adic groups, via graded Hecke algebras and equivariant homology. He will also continue the study of the parameter space of these representations from the point of view of intersection cohomology. Further, he will study canonical bases in enveloping algebras and the total positivity in reductive groups over the reals. Many different algebraic objects can be represented as algebraic sets of transformations of other algebraic objects. Through these representations their structure can be determined. This project is concerned with the representation theory of certain algebras. The study of these algebras has applications throughout mathematics and mathematical physics.

该奖项支持有关仿射Hecke代数和量子组的代表理论的研究。 首席研究者将通过分级的Hecke代数和均值同源性完成分类半拆分P-ADIC群体的不受影响表示的分类。 他还将从交叉点的角度继续研究这些表示的参数空间。 此外，他将研究构成代数的规范基础，以及对真实组的还原群体的总阳性。 许多不同的代数对象可以表示为其他代数对象的代数转换集。 通过这些表示，可以确定它们的结构。 该项目与某些代数的表示理论有关。 这些代数的研究在整个数学和数学物理学中都有应用。