L-Packets of Representations of P-Adic Groups

9972579里德教授将试图明确地描述和计算应与给定L-包的表示共享的表示的属性和数值不变量。 他预计，他可以处理不变量一样的分歧，正式程度，Plancherel措施，领先的K型和相关的无穷小字符这项工作预计将产生影响的其他领域目前数论研究一样的椭圆几何的p进群，并研究水平零朗兰兹对应。 科学家们早就知道，研究一个物体的有效方法，无论是数学的还是其他的，就是研究它的对称性。 数学家们已经将这个简单的想法发展成一个普遍的理论，在这个理论中，数学对称性被推广并排列成它们自己的数学对象，称为群。 一旦这个抽象的过程构造了对称性，通过用更熟悉的对象来表示它们，这些组就被带回到更具体的设置中。 因此表示论成为数学家和其他科学家的一个非常重要的工具。 里德博士打算通过研究通过这种上下过程产生的表示论的明确例子来研究数字的一些基本结构。

9972579Professor Reeder will attempt to describe and calculate explicitly properties and numerical invariants of representations that should be shared with the representations of a given L-packet. He expects that he can deal with invariants like the ramification, the formal degrees, Plancherel measures, leading K-types and associated infinitesimal characters This work is expected to have impact on other areas of current number theory research like the elliptic geometry of p-adic groups, and the study of level zero Langlands correspondence. Scientists have long known that an effective way to study an object, mathematical or otherwise, is to study its symmetries. Mathematicians have developed this simple idea into a general theory in which mathematical symmetries are generalized and arranged into their own mathematical object called a group. Once this process of abstraction has structured the symmetries, the groups are brought back to a more concrete setting by representing them in terms of more familiar objects. Thus Representation Theory becomes a very important tool for mathematicians and other scientists. Dr. Reeder intends to study some of the basic structures of numbers by studying explicit examples of the representation theory that arise through this up and down process.