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.

表示理论是使用可逆矩阵组的代数研究对称性的代数分支，尤其是线性数学结构的对称性。在此项目中，线性结构本身是有限的矩阵组，或更一般的矩阵组，其条目满足固定质量数量的分裂性能。几何技术和组合技术将被带到研究这些群体的表示形式中，尤其是在代表矩阵本身具有满足可划分性能的条目时的重要情况下。 该研究项目将推进还原代数群体的代表理论。 PI将研究使用分类中心概念的有前途的新方法，以及与单一表示和性格束相关的问题，Hecke代数的规范基础，P-Adic群体的“几乎字符”以及与参与相关的W-Graphs。