Tamely Ramified Langlands Correspondence

驯服的分枝朗兰通讯

• 批准号: 0207231
• 负责人: Mark Reeder
• 金额: $ 10.48万
• 依托单位: Boston College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-06-01 至 2005-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0207231&HistoricalAwards=false
• 关键词: Tamely; Ramified; Langlands; Correspondence

The investigator attempts to classify square-integrable tamely ramified representations of split reductive p-adic groups G and their inner forms, by means of homomorphisms from the tame Weil-Deligne group into the dual group of G. This project is part of the local Langlands conjecture for such groups. The representations are partitioned into finite sets, called ``L-packets". The method is a p-adic analogue of Lusztig's Jordan decomposition for finite reductive groups. From a functorial point of view, the tame L-packets are bijective lifts of unipotent L-packets for quasi-split groups and their inner forms. Properties of the L-packets, such as formal degrees and Whittaker models, will also be investigated.Symmetry is an effective way to study mathematical and physical objects. A Group is a collection of symmetries, and Representation Theory is the study of how these symmetries manifest in different ways. As a simple example, there is a group of sixty symmetries consisting of permutations of five objects, and this group also manifests as the sixty symmetries of an icosohedron, and of the fullerene molecule. The investigator studies certain infinite groups of infinite dimensional symmetries. In the past forty years, mathematicians and physicists have guessed that there may be deep relations between such symmetries and fundamental, as yet undiscovered, properties of numbers. The investigator attempts to confirm part of these conjectures, and make them more explicit.

研究者试图通过从驯服的Weil-Deligne群到G的对偶群的同态，对分裂约化p-adic群G的平方可积驯服分歧表示及其内部形式进行分类.这个项目是局部朗兰兹猜想的一部分，这样的群体。这些表示被划分成有限的集合，称为“L-分组”。该方法是一个p-adic模拟Lusztig的约旦分解有限约化群。从函子的观点来看，驯服L-包是拟分裂群及其内部形式的幂幺L-包的双射提升。对称性是研究数学和物理对象的有效方法。群是对称性的集合，而表征论是研究这些对称性如何以不同的方式表现出来。举一个简单的例子，有一个由五个物体的排列组成的60个对称的群，这个群也表现为二十面体和富勒烯分子的60个对称。研究人员研究某些无限群的无限维对称性。在过去的40年里，数学家和物理学家们猜测，这种对称性与数字的基本性质之间可能存在着深刻的联系，但这些性质尚未被发现。调查人员试图证实这些陈述的一部分，并使其更加明确。