Characters and related distributions on reductive p-adic groups, distinguised representations

还原 p 进群上的特征和相关分布，可区分表示

• 批准号: 155502-2007
• 负责人: Murnaghan, Fiona
• 金额: $ 1.46万
• 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: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=476070
• 关键词: Characters; related; distributions; reductive; adic

This proposal involves the study of representations of reductive p-adic groups. These groups are matrix groups whose matrix entries belong to certain fields that are important in number theory. There are three different components to the proposed research. The first component involves finding ways to classify some of the representations of p-adic groups. The current classification of some families of representations appears to be more complicated than it needs to be, and we plan to investigate ways of simplifying the classification. The second component involves studying properties of the characters of representations of reductive p-adic groups. The characters are functions that play an important role in harmonic analysis on p-adic groups. Our goal is to derive new formulas for the characters of particular kinds of representations. The third component involves the study of spherical characters of distinguished representations. Such representations have nice symmetry properties relative to involutions of the group. We hope to find formulas for spherical characters of some families of distinguished representations.

这个建议涉及到研究约化p进群的表示。这些群是矩阵群，其矩阵元素属于数论中重要的某些领域。拟议的研究有三个不同的组成部分。第一部分涉及找到方法来分类p-adic群的一些表示。目前对某些表示族的分类似乎比它需要的要复杂，我们计划研究简化分类的方法。第二部分是研究约化p-adic群表示的特征标的性质。特征标是在p-adic群的调和分析中起重要作用的函数。我们的目标是导出特殊类型的表征的新公式。第三部分涉及研究的球形字符的区别表示。这样的表示相对于群的对合具有很好的对称性。我们希望找到一些特殊表示族的球面特征标的公式。