酉群的Gan-Gross-Prasad猜想的一个局部迹公式:阿基米德情况

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

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引用次数: 17

摘要

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。

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

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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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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.