Branching of Automorphic Fundamental Solutions

A reciprocal branching problem for automorphic representations and global Vogan packets

Let $G$ be a group and $H$ be a subgroup of $G$. The classical branching rule (or symmetry breaking) asks: For an irreducible representation $π$ of $G$, determine the occurrence of an irreducible representation $σ$ of $H$ in the restriction of $π$ to $H$. The reciprocal branching problem of this classical branching problem is to ask: For an irreducible representation $σ$ of $H$, find an irreducible representation $π$ of $G$ such that $σ$ occurs in the restriction of $π$ to $H$. For automorphic representations of classical groups, the branching problem has been addressed by the well-known globa…

Bessel Descents and Branching Problems

We discuss the theory of automorphic descents of Bessel type and its relation to automorphic version of branching problem and its relevant reciprocal branching problem.

计算GL2（Qp）的Bruhat-Tits树的基本区，p-adic自守形式和Shimura曲线的规范嵌入

Computing fundamental domains for the Bruhat-Tits tree for GL2(Qp), p-adic automorphic forms, and the canonical embedding of Shimura curves

我们描述了一个算法，用于计算某些四元数的Bruhat-Tits树GL 2（QP）。作为应用，我们描述了一个算法，以获得（几何）方程的正则嵌入的志村曲线。

Hitchin type moduli stacks in automorphic representation theory

In the study of automorphic representations over a function field, Hitchin moduli stack and its variants naturally appear and their geometry helps the comparison of trace formulae. We give a survey on applications of this observation to a relative fundamental lemma, the arithmetic fundamental lemma and to the higher Gross-Zagier formula.

由基本傅里叶系数确定模形式

Determination of modular forms by fundamental Fourier coefficients

本文是基于作者在2012年孟买TIFR举行的自守表示和L-函数国际学术讨论会上的演讲的研究阐述。我们考虑以下问题的一些特殊情况：当是一个自然的子集的傅里叶系数足以唯一地确定一个“模形式“？本文考虑两类模形式：a）半整权的经典模形式和b）亏格为2且权为整的Siegel模形式.这两个明显不同的情景原来是密切相关的。我们的研究结果的动机，并有几个有趣的连接，自守L-函数和贝塞尔模型。

关于对称空间格点与自守谱的一个精确公式

An exact formula relating lattice points in symmetric spaces to the automorphic spectrum

我们从谱恒等式中提取了复半单对称空间的扩张区域中的格点数目与自守谱之间的精确关系式，该谱恒等式是通过产生不变微分算子（Delta-lambda_z）^N的自守基本解的两个表达式而得到的.一方面，我们利用双K不变函数的调和分析，在自由空间G/K上得到相应的微分方程的解，并将其构造成Poincare级数。另一方面，本文发展的一个合适的整体自守Sobolev理论，使我们能够使用自守形式的调和分析来产生自守谱的解。