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arXiv · 1203.0039

Periods and harmonic analysis on spherical varieties

Yiannis Sakellaridis·Akshay Venkatesh
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Abstract

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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Yiannis Sakellaridis, Akshay Venkatesh. 2012-02-29. Periods and harmonic analysis on spherical varieties. https://arxiv.org/abs/1203.0039

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