Mathematical Sciences: Theta Lifting and Cohomology of Discrete Subgroups

本研究在自同构形式领域，利用theta-升降机来构造与群在局部域上的表示理论相关的自同构形式。虽然局部表示理论的学者们已经在提升一般类的酉表示方面取得了深入的成果，但在自同构形式上的应用往往局限于提升一维字符。本研究涉及全球举升问题的一个具体而重要的案例，其成功将为今后更多的一般性工作提供指导。本研究将现代分析、代数和数论结合起来，研究经典群的表示理论和经典群上的自同构形式。

This research, in the area of automorphic forms, makes use of theta-liftings for the construction of automorphic forms related to the representation theory of groups over local fields. Although scholars in local representation theory have obtained deep results about lifting general classes of unitary representations, the applications to automorphic forms have often been restricted to lifting one-dimensional characters. This research involves a specific and important case of the global lifting problem and success should provide guidance for more general work in the future. This research bridges both Modern Analysis and Algebra and Number Theory and concerns the representation theory of classical groups together with automorphic forms on classical groups.