Unitary Representations of Reductive P-Adic Groups

摘要Savin DMS-9803806 MUIC将研究经典的和某些例外的约化p-进李群的酉表示，重点是在数论中的应用。这将包括对诱导表示和互补级数的可约性的研究。他还将调查孤立么正表示的构造。李群理论是以挪威数学家索菲斯·李的名字命名的，一直是20世纪数学的主要主题之一。作为利用系统固有对称性的数学工具，李群的么正表示理论对数学本身产生了深远的影响，例如在数论中，对理论物理，特别是量子力学和基本粒子物理产生了深远的影响。

Abstract Savin DMS-9803806 Muic will investigate unitary representations of classical and certain exceptional reductive p-adic Lie groups, with emphasis on applications in number theory. This will include investigations of reducibility of induced representations and complementary series. He will also investigate a construction of isolated unitary representations. The theory of Lie groups, named after the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the theory of unitary representations of Lie groups has had a profound impact upon mathematics itself, for example in number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.