论文标题
多重性和plancherel公式，用于非等级Hermitian矩阵的空间
Multiplicities and Plancherel formula for the space of nondegenerate Hermitian matrices
论文作者
论文摘要
本文包含两个关于光谱分解的结果，从广义上讲，在特征零的局部领域，非等级遗传学矩阵的空间。第一个是相关的$ l^2 $空间的明确平行分解，因此在这种情况下确认了sakellaridis-venkatesh的猜想。第二个是在$ p $ - adiC的情况下的多个通用表示的公式，该案例扩展了Feigon-lapid-offen的先前工作。这两个结果均根据Arthur-Clozel的二次局部基础变化表示，这些证明基于Jacquet和Ye先前研究的两个相对痕量公式的局部类似物，并称为（相对）Kuznetsov痕量公式。
This paper contains two results concerning the spectral decomposition, in a broad sense, of the space of nondegenerate Hermitian matrices over a local field of characteristic zero. The first is an explicit Plancherel decomposition of the associated $L^2$ space thus confirming a conjecture of Sakellaridis-Venkatesh in this particular case. The second is a formula for the multiplicities of generic representations in the $p$-adic case that extends previous work of Feigon-Lapid-Offen. Both results are stated in terms of Arthur-Clozel's quadratic local base-change and the proofs are based on local analogs of two relative trace formulas previously studied by Jacquet and Ye and known as (relative) Kuznetsov trace formulas.
