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.

******我的研究构成了Langlands计划的一部分，Langlands计划是数学理论，自动形式，表示理论和代数几何形状之间的数学分支***。 我研究某些矩阵组的表示的特性***，称为还原性P-ADIC组。这些矩阵组以***数字理论术语定义 - 矩阵条目属于p -adic字段 - 这些字段是数字***字段（有限的有限扩展）的非一切本完成。近年来，对谐波分析的兴趣很大。我的工作涉及***的研究和构建还原性P-ADIC群体的杰出表示。这些杰出的表示***相对于定义p-adic对称空间的相关性表现出特定的对称性。我的主要重点是构建相对超级的表示及其特性的研究，尤其是与兰兰兹计划相关的代表。