Periods and harmonic analysis on spherical varieties
By Y. Sakellaridis, Akshay Venkatesh. Astérisque, 2012
249 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/01784fecdda6ba09154490cc5b91e91b07279513
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A `relative' local Langlands correspondence (2015, background): “\G), say for spectral decomposition, for suitably chosen subgroups Hof a reductive group G, of what the ‘usual’ Langlands program is for L2(G); see for instance the work of Sakellaridis and Venkatesh [Sa-V] where the authors setup a large framework to deal with this question in considerable generali”