课题基金 / 基金详情

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

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:
$19.0万
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
项目状态:
已结题
起止时间:
2016-09-01 至 2019-08-31

项目摘要

项目成果

George Lusztig的其他基金

相似基金

相关文献

中文摘要
翻译
表示论是代数的一个分支,利用可逆矩阵群研究对称,特别是线性数学结构的对称。在这个项目中,线性结构本身是有限矩阵群,或者更一般地,其条目满足关于固定素数的可除性的矩阵群。几何和组合技术将被用来研究这些群的表示,特别是在表示矩阵本身具有满足可除性性质的项的重要情况下。这项研究将对约化代数群的表示理论起到推动作用。PI将研究使用范畴中心概念的一种很有前途的新方法所产生的问题,以及与幂等表示和特征标组、Hecke代数的标准基、p-进群的“几乎特征标”以及与对合相关的W-图有关的问题。
英文摘要
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.
期刊论文(0)
专著(0)
科研奖励(0)
会议论文
Representations of finite reductive groups, character sheaves and theory of total positivity
Geometric Methods in the Representation Theory of Affine Hecke Algebras, Finite Reductive Groups, and Character Sheaves
Representations of Reductive Groups, May 19-23, 2014.
Mathematical Sciences: Geometric methods in the representation theory of affine Hecke algebras, finite reductive groups and character sheaves
国内基金
海外基金
Computational Methods for Analyzing Toponome Data