Mathematical Sciences: Representation Theory

该项目的研究将由两名调查人员进行，他们是首席调查员Herve Jacquet和他的博士后伙伴Michael Heumos。Jacquet将继续努力推广他的新跟踪公式。关于L函数特殊值的结果，确定一般线性群的剩余谱以及更好地理解Weil表示是该项目的长期目标之一。Heumos将研究p-add场上Gln的么正表示的模型。这些模型推广了标准的Whittaker模型，是GLN的子群。例如，也许所有的么正表示都唯一地嵌入到一个唯一的模型中。这将为研究p-addGln的么正表示提供一个新的视角，并具有广泛的应用前景。这项研究属于数论领域，俗称“朗兰氏计划”。它运用了许多领域的先进概念，尤其是现代分析，来回答算术中的基本问题。

The research on this project will be carried out by two investigators, the principal investigator Herve Jacquet and his postdoctoral associate Michael Heumos. Jacquet will continue his efforts at generalizing his new trace formula. Results on special values of L-functions, the determination of the residual spectrum of the general linear group and a better understanding of the Weil representation are among the long range goals of the project. Heumos will study models for unitary representations of GLn over a p-adic field. These models generalize the standard Whittaker model and are subgroups of GLn. Examples suggest that perhaps all unitary representations embed uniquely in a unique model. This would provide a new perspective to the study of unitary representations of the p-adic GLn and would have widespread applications. This research is in the area of number theory commonly known as the "Langland's program". It applies advanced notions from many areas, most especially modern analysis, to answer fundamental questions in arithmetic.