Harmonic analysis over Chevalley groups and number theory

Chevalley 群和数论的调和分析

• 批准号: 2603416
• 金额: --
• 依托单位: University of Nottingham
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2603416
• 关键词: Harmonic; analysis; over; Chevalley; groups

This PhD project will be aiming at generalizing Deligne-Lustig theory and Springer correspondence to arbitrary Chevalley groups. The project may start with extending these theories to some classical groups such as symplectic groups and orthogonal groups. The Hecke algebras defined on general linear groups over arbitrary fields will also be studied. The study of representations of Chevalley groups has many applications to number theory, such as automorphic forms and p-adic analysis. It also helps to seek the some interplays among symmetric groups, general linear groups over local fields and finte fields, which may finally linked to Langlands correspondence

这个博士项目的目的是将Deligne-Lustig理论和Springer对应推广到任意Chevalley群。该项目可能会从将这些理论扩展到一些经典群，如辛群和正交群开始。定义在任意域上的一般线性群上的Hecke代数也将被研究。Chevalley群的表示研究在数论中有许多应用，例如自守形式和p-adic分析。它还有助于寻找对称群、局部域上的一般线性群和有限域之间的一些相互作用，这些相互作用最终可能与朗兰兹对应联系起来