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: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=675396
• 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.

*我的研究是朗兰兹计划的一部分，兰兰兹计划是数学的一个分支，涉及数论、自同构形、表示论和代数几何之间的深层联系。我研究了某些被称为约化p-进群的矩阵群的表示的*性质。这些矩阵群定义在数论的*项中--矩阵项属于p-ady域--这些域是数*域(有理数的有限扩张)的非阿基米德补全。近年来，关于p进对称簇的调和分析及其与朗兰兹程序的联系引起了人们极大的兴趣。我的工作涉及*研究和构造约化p-进群的区别表示。这些区别表示*表现出相对于定义p-进对称空间的对合的特定对称性质。*区别表示理论中的基本构件是所谓的相对超尖*表示。我的主要关注点是相对超尖球面表示的构造及其性质的研究，*特别是那些与朗兰兹计划相关的性质。