AST418 - A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the archimedean case

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2015-06-04 DOI:10.24033/ast.1120

Raphael Beuzart-Plessis

引用次数: 17

Abstract

In this paper, we prove, following earlier work of Waldspurger ([Wa1], [Wa4]), a sort of local relative trace formula which is related to the local Gan-Gross-Prasad conjecture for unitary groups over a local field $F$ of characteristic zero. As a consequence, we obtain a geometric formula for certain multiplicities $m(\pi)$ appearing in this conjecture and deduce from it a weak form of the local Gan-Gross-Prasad conjecture (multiplicity one in tempered L-packets). These results were already known over $p$-adic fields and thus are only new when $F=\mathbb{R}$.

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酉群的Gan-Gross-Prasad猜想的一个局部迹公式:阿基米德情况

本文继Waldspurger ([Wa1]， [Wa4])的早期工作之后，证明了特征为零的局部域$F$上的酉群的一类与局部Gan-Gross-Prasad猜想有关的局部相对迹公式。因此，我们得到了该猜想中出现的某些多重性$m(\pi)$的几何公式，并由此推导出局部Gan-Gross-Prasad猜想的弱形式(调和l包中的多重性1)。这些结果在$p$-adic字段中是已知的，因此只有当$F=\mathbb{R}$时才是新的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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