Geometric Methods in the Representation Theory of Affine Hecke Algebras, Finite Reductive Groups, and Character Sheaves

仿射 Hecke 代数、有限还原群和特征轮表示论中的几何方法

• 批准号: 1566618
• 负责人: George Lusztig
• 金额: $ 19万
• 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: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1566618&HistoricalAwards=false
• 关键词: Geometric; Methods; Representation; Theory; Affine

Representation theory is a branch of algebra studying symmetries, especially symmetries of linear mathematical structures, using groups of invertible matrices. In this project the linear structures are themselves finite matrix groups, or more generally matrix groups whose entries satisfy divisibility properties with respect to a fixed prime number. Geometrical and combinatorial techniques will be brought to bear to study representations of these groups, especially in the important case when the representing matrices themselves have entries that satisfy divisibility properties. This research project will advance the representation theory of reductive algebraic groups. The PI will study questions stemming from a promising new method using the notion of categorical centers, as well as questions related to unipotent representations and character sheaves, canonical bases of Hecke algebras, "almost characters" of p-adic groups, and W-graphs associated to involutions.

表示论是代数的一个分支，利用可逆矩阵群来研究对称性，特别是线性数学结构的对称性。在这个项目中，线性结构本身是有限矩阵组，或者更一般地，其条目满足相对于固定素数的整除性质的矩阵组。几何和组合技术将用于研究这些群的表示，特别是在表示矩阵本身具有满足整除性质的条目时的重要情况。 该研究项目将推进还原代数群的表示理论。 PI 将研究源自一种使用分类中心概念的有前途的新方法的问题，以及与单能表示和字符轮、Hecke 代数的规范基、p 进群的“几乎字符”和 W 图相关的问题与卷合有关。