Distinguished representations of reductive p-adic groups

还原p进群的杰出表示

• 批准号: RGPIN-2017-06066
• 负责人: Murnaghan, Fiona
• 金额: $ 1.02万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=712029
• 关键词: Distinguished; representations; reductive; adic; groups

My research forms part of the Langlands program, a branch of mathematics involving deep connections between number theory, automorphic forms, representation theory, and algebraic geometry. I study the properties of representations of certain matrix groups known as reductive p-adic groups. These matrix groups are defined in terms of number theory - the matrix entries belong to p-adic fields - these fields are nonarchimedean completions of number fields (finite extensions of the rational numbers). In recent years, there has been considerable interest in harmonic analysis on p-adic symmetric varieties and connections with the Langlands program. My work involves the study and construction of distinguished representations of reductive p-adic groups. These distinguished representations exhibit specific symmetry properties relative to the involution that defines the p-adic symmetric space. The basic building blocks in the theory of distinguished representations are the so-called relatively supercuspidal representations. My main focus is on construction of relatively supercuspidal representations and the study of their properties, particularly those that are relevant to the Langlands program.

我的研究是朗兰兹纲领的一部分，朗兰兹纲领是数学的一个分支，涉及到深层的联系 在数论自守形式表示论和代数几何之间。 我研究了 某些矩阵群的表示称为约化p进群。这些矩阵组定义在 数论术语-矩阵元素属于p-adic域-这些域是数的非阿基米德完备化 域（有理数的有限扩展）。近年来，谐波分析引起了人们的极大兴趣 关于p-adic对称簇和与朗兰兹程序的联系。我的工作包括 研究和构造约化p进群的特殊表示。这些杰出的代表 相对于定义p-adic对称空间的对合展现出特定的对称性质。 区别表示理论的基本组成部分是所谓的相对超尖点 表示。我的主要重点是相对超尖点表示的构造及其性质的研究， 尤其是那些与朗兰兹纲领有关的