仿射Hecke代数与Hiraga，Ichino和Ikeda的结构
Affine Hecke algebras and the conjectures of Hiraga, Ichino and Ikeda
摘要：
Hiraga，Ichino和Ikeda用局部Langlands参数给出了局部域$F$上约化群的点群的Plancherel密度的一个显式表达式.在这些讲座中，我们将提出一个证明这些命题为Lusztig的类表示的单幂约，如果$F$是$p$ -进和$G$是伴随型和分裂的一个非分歧扩张的$F$。这是基于作者的论文[Spectral transfer morphisms for unipotent affine Hecke algebras，Selecta Math.（N.S.）22（2016），no. 4，2143- 2207]。更一般地为$G$连接还原（仍然假设是分裂的一个非分歧扩张的$F$），我们将表明，要求的兼容性与平贺，一野和池田的结构基本上决定了Langlands参数化的调和表示的幂幺约化。我们将表明，存在参数化，其中平贺，一野和池田的结构举行了合理的常数因子。主要的技术工具是光谱之间的转移映射的规范化仿射Hecke代数中使用的同前。
英文摘要：
Hiraga, Ichino and Ikeda have conjectured an explicit expression for the Plancherel density of the group of points of a reductive group defined over a local field $F$, in terms of local Langlands parameters. In these lectures we shall present a proof of these conjectures for Lusztig's class of representations of unipotent reduction if $F$ is $p$-adic and $G$ is of adjoint type and splits over an unramified extension of $F$. This is based on the author's paper [Spectral transfer morphisms for unipotent affine Hecke algebras, Selecta Math. (N.S.) 22 (2016), no. 4, 2143--2207]. More generally for $G$ connected reductive (still assumed to be split over an unramified extension of $F$), we shall show that the requirement of compatibility with the conjectures of Hiraga, Ichino and Ikeda essentially determines the Langlands parameterisation for tempered representations of unipotent reduction. We shall show that there exist parameterisations for which the conjectures of Hiraga, Ichino and Ikeda hold up to rational constant factors. The main technical tool is that of spectral transfer maps between normalised affine Hecke algebras used in op. cit.
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