L-Packets of Representations of P-Adic Groups

9972579 Reeder教授将尝试明确地描述和计算表征的性质和数值不变量，这些表征应该与给定l包的表征共享。他期望他能够处理不变量，如分支，形式度，Plancherel测度，领先的k型和相关的无穷小特征。这项工作有望对当前数论研究的其他领域产生影响，如p进群的椭圆几何和零能级朗兰兹对应的研究。科学家们早就知道，研究一个物体的有效方法，无论是数学上的还是其他方面的，就是研究它的对称性。数学家们已经把这个简单的想法发展成一个普遍的理论，在这个理论中，数学对称性被一般化，并被安排成他们自己的数学对象，称为群。一旦这个抽象过程构建了对称性，通过用更熟悉的对象来表示它们，这些群体就会回到更具体的环境中。因此表征理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在这个上下过程中产生的表示法理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.