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Paley-Wiener Theorems for a P-Adic Spherical Variety

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Paley-Wiener Theorems for a P-Adic Spherical Variety Synopsis

"Let SpXq be the Schwartz space of compactly supported smooth functions on the p-adic points of a spherical variety X, and let CpXq be the space of Harish- Chandra Schwartz functions. Under assumptions on the spherical variety, which are satisfied when it is symmetric, we prove Paley-Wiener theorems for the two spaces, characterizing them in terms of their spectral transforms. As a corollary, we get relative analogs of the smooth and tempered Bernstein centers - rings of multipliers for SpXq and C pXq. When X " a reductive group, our theorem for CpXq specializes to the well-known theorem of Harish-Chandra, and our theorem for SpXq corresponds to a first step - enough to recover the structure of the Bernstein center - towards the well-known theorems of Bernstein [Ber] and Heiermann [Hei01]"--.

About This Edition

ISBN: 9781470444020
Publication date:
Author: Patrick Delorme, Pascale Harinck, Yiannis Sakellaridis
Publisher: American Mathematical Society
Format: Paperback
Series: Memoirs of the American Mathematical Society
Genres: Algebraic geometry
Algebra