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-adic约化群的所有表示。 它仍然需要澄清是什么参数化这些类型。 此外，PI希望了解类型与朗兰兹参数的关系。 此外，本项目还研究了部分Bessel函数和局部系数理论中的Bruhat分解问题，这些问题都是Langlands程序的一部分，Langlands程序是数学中最有影响力的程序之一，将数论和分析联系起来。这里的表示论问题处理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.