L-Packets of Representations of P-Adic Groups

点击翻译按钮获取中文摘要

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.