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A local relative trace formula for spherical varieties

Ioan Filip

Title:
A local relative trace formula for spherical varieties
Author(s):
Filip, Ioan
Thesis Advisor(s):
Zhang, Wei
Date:
Type:
Theses
Degree:
Ph.D., Columbia University
Department(s):
Mathematics
Persistent URL:
Abstract:
Let F be a local non-Archimedean field of characteristic zero. We prove a Plancherel formula for the symmetric space GL(2,F)\GL(2,E), where E/F is an unramified quadratic extension. Our method relies on intrinsic geometric and combinatorial properties of spherical varieties and constitutes the local counterpart of the global computation of the Flicker-Rallis period as a residue of periods against Eisenstein series. We also give a novel derivation of the Plancherel formula for the strongly tempered variety T\PGL(2) over F (with maximal split torus T) using a canonical smooth asymptotics morphism and a contour shifting method. In this rank one local setting, our proof is similar to Langlands' proof over global fields describing the spectrum of a reductive group in terms of residues of Eisenstein series. Finally, using both L2-decompositions, we develop a local relative trace formula and outline a comparison result in the setting of the unitary rank one Gan-Gross-Prasad conjecture.
Subject(s):
Combinatorial geometry
Geometry, Algebraic
Mathematics
Trace formulas
Item views
378
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Suggested Citation:
Ioan Filip, , A local relative trace formula for spherical varieties, Columbia University Academic Commons, .

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