球形品种的周期和谐波分析

IF 1 4区数学 Q1 MATHEMATICS

Asterisque Pub Date : 2012-02-29 DOI:10.24033/ast.1040

Y. Sakellaridis, Akshay Venkatesh

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引用次数: 194

摘要

给定群G在非阿基米德局部域k上的球形变化X, L^2(X)的Plancherel分解应与将Arthur参数“区分”为与Gaitsgory和Nadler定义的对偶群密切相关有关。在此基础上，我们在对球变分的一些假设下，建立了L^2(X)直至其“边界退化”的离散(模中心)谱的Plancherel公式。最后，我们讨论了关于球面子群上自同构形式的周期积分的局部猜想的全局类似。

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Periods and harmonic analysis on spherical varieties

Given a spherical variety X for a group G over a non-archimedean local field k, the Plancherel decomposition for L^2(X) should be related to "distinguished" Arthur parameters into a dual group closely related to that defined by Gaitsgory and Nadler. Motivated by this, we develop, under some assumptions on the spherical variety, a Plancherel formula for L^2(X) up to discrete (modulo center) spectra of its "boundary degenerations", certain G-varieties with more symmetries which model X at infinity. Along the way, we discuss the asymptotic theory of subrepresentations of C^{infty}(X), and establish conjectures of Ichino-Ikeda and Lapid-Mao. We finally discuss global analogues of our local conjectures, concerning the period integrals of automorphic forms over spherical subgroups.

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来源期刊

Asterisque MATHEMATICS-

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

>12 weeks

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