Automorphic Plancherel density theorem
Automorphic Plancherel density theorem
复制标题
自守 Plancherel 密度定理
DOI：
10.1007/s11856-012-0018-z
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发表时间：
2012
影响因子：
1
通讯作者：
S. Shin
中科院分区：
文献类型：
--
作者：
S. Shin
设F是全真实的域，G是F上的连通约化群，S是F的有限位的有限集.假设G（F）有一个离散级数表示。基于Sauvageot，Serre，Conrey-Duke-Farmer等人的工作，我们证明了$$G\left（{\mathbb{A}_F } \right）$$的尖点自守表示的S-分量在适当的意义下关于G（FS）的酉对偶上的Plancherel测度是等分布的.给出了一些应用，如整体尖点谱中局部表示的极限重数公式和具有给定局部性质的尖点自守表示的一个相当灵活的存在定理.当F不是一个全真实的域或G（F ∈ N）没有离散级数时，我们给出了上述结果的一个较弱的版本.
Let F be a totally real field, G a connected reductive group over F, and S a finite set of finite places of F. Assume that G(F ⊗ℚ ℝ) has a discrete series representation. Building upon work of Sauvageot, Serre, Conrey-Duke-Farmer and others, we prove that the S-components of cuspidal automorphic representations of $$G\left( {\mathbb{A}_F } \right)$$ are equidistributed with respect to the Plancherel measure on the unitary dual of G(FS) in an appropriate sense. A few applications are given, such as the limit multiplicity formula for local representations in the global cuspidal spectrum and a quite flexible existence theorem for cuspidal automorphic representations with prescribed local properties. When F is not a totally real field or G(F ⊗ℚ ℝ) has no discrete series, we present a weaker version of the above results.