Representations and Types of p-adic Groups

PI和J. Kim最近的工作提供了足够的类型来分类许多p进约化群的所有表示。是什么使这些类型参数化还有待澄清。此外，PI想要了解类型是如何与朗兰兹参数相关的。此外，该项目还寻求研究与部分贝塞尔函数和局部系数理论中出现的Bruhat分解相关的问题。这些问题都是朗兰兹程序的一部分，朗兰兹程序是数学中最有影响力的程序之一，将数论和分析联系在一起。这里的表示理论问题涉及程序中的一些局部分析，并且与算术和几何有很深的联系。

Recent work of the PI and J. Kim provides enough types to classify all representations of many p-adic reductive groups. It remains to clarify what parametrizes those types. Moreover, the PI would like to understand how types are related to Langlands parameters. In addition, the project seek to study a problem related to Bruhat decomposition which arises in the theory of partial Bessel functions and local coefficients.These problems are all part of the Langlands program, one of the most influence programme in mathematics linking number theory and analysis. The representation theory problems here deal with some of the local analysis in the program, and have deep connections with arithmetic and geometry.