Period integrals

摘要Jacquet DMS-0245310 PI建议研究自守表示空间上定义的某些周期积分。两个主要问题是确定哪些表示的周期是非零的，如果可能的话，用局部数据来表示周期（全局定义的）。本研究的主要工具是相对痕量公式，其研究由PI发起。其中一个主要的困难是代数组合恒等式（基本引理）。最近，PI获得了有关身份是一个有趣的案例。从更广的角度来看，Langlands程序处理了某些线性算子在约化群上的自守函数空间上的调和分析。特征值与具有显著解析性质的L-函数有关。另一方面，与不同组相关联的本征值以简单的方式相关。在某些特定情况下，这两种关系可以变得更精确和更几何。该提案的目的是研究这些具体案例。

Abstract for Jacquet DMS-0245310The PI proposes to study certain period integrals defined on spaces of automorphic representations. The two main questions are to determine for which representations the periods are non-zero, and to express if possible the periods (which are globally defined) in terms of local data. The main tool of this investigation is the relative trace formula, the study of which was initiated by the PI. One of the main difficulties is a conjectural combinatorial identity (the fundamental lemma). Recently, the PI has obtained the identity in question is an interesting case. The method may apply to other cases as well.From a broader perspective, Langlands program deals with the harmonic analysis of certain linear operators on the spaces of automorphic functions defined on reductive groups. The eigenvalues are related to L-functions with striking analytic properties. On the other hand, the eigenvalues associated with different groups are related in a simple way. In certain specific cases, the two types of relations can be made more precise and more geometric. The goal of the proposal is to study these specific cases.