自同构$L$ \snug -函数、交织算子和$p$ \snug -进群的不可约调和表示
Automorphic $L$\snug-functions, intertwining operators, and the irreducible tempered representations of $p$\snug-adic groups
摘要：
本文对连通约化$p$ -adic群的交织算子理论及其与自守$L$ -函数的联系作了简要的说明。目的是说明调和分析与算术的关系。特别是，我们描述了如何理论的Plancherel措施，使我们能够计算某些地方朗兰兹$L$ -功能。为了更完备，我们对朗兰兹纲领作一个简单的介绍。理论的$R$ -群和椭圆表示处理在这里以及。最后，我们给出了一个例子，说明如何扭曲的内窥镜的理论起着至关重要的作用，在确定两个交织运营商和本地朗兰兹$L$ -功能的问题。这份手稿的修订版将作为一个章节出现在“Teoria de Representaciones de Groupos Algebraicos Sobre Cuerpos Locales y Applications”（C. Bushnell，P. Kutzko，J. Pantoja，J. Soto Andrade编辑）。
英文摘要：
We give an expository account of the theory of intertwining operators for connected reductive $p$--adic groups, and their connection with automorphic $L$--functions. Our purpose is to illustrate the relation between harmonic analysis and arithmetic. In particular, we describe how the theory of Plancherel measures allows us to compute certain local Langlands $L$--functions. In order to be more self contained, we give a brief introduction to the Langlands program. The theory of $R$--groups and elliptic representations is treated here as well. Finally, we give an example which illustrates how the theory of twisted endoscopy plays a crucial role in determining the poles of both the intertwining operators and the local Langlands $L$--functions in question. A version of this manuscript, in revised form, will appear as a chapter in the proceedings of the conference ``Teoria de Representaciones de Groupos Algebraicos Sobre Cuerpos Locales y Applicationes'' (C. Bushnell, P. Kutzko, J. Pantoja, J. Soto Andrade eds.).
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