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.

该奖项支持仿射赫克代数和量子群表示论的研究。 首席研究员将致力于通过分级 Hecke 代数和等变同调来完成半简单分裂 p-adic 群的未分支表示的分类。 他还将继续从交交上同调的角度研究这些表示的参数空间。 此外，他还将研究包络代数中的规范基以及实数还原群中的总正性。 许多不同的代数对象可以表示为其他代数对象的变换的代数集。 通过这些表示可以确定它们的结构。 该项目涉及某些代数的表示论。 这些代数的研究在整个数学和数学物理中都有应用。