Title: Paley-Wiener theorems for p-adic spherical varieties
Speaker: Yiannis Sakellaridis (Rutgers University at Newark)
Abstract: For a reductive p-adic group H, the description of the Bernstein center of the category of smooth H-representations is equivalent to the description of H x H-endomorphisms of the space of smooth, compactly supported functions on H, and the Bernstein decomposition corresponds to an H x H-equivariant decomposition of this space. The goal of this talk is to generalize this decomposition when H is replaced by a spherical variety X satisfying some strong assumptions (which cover all symmetric cases). In parallel, we will discuss the spectral transform of the space of Harish-Chandra Schwartz functions on X, generalizing Harish-Chandra's description for X=H. This is joint work with Patrick Delorme and Pascale Harinck.
Seminar URL: https://research.math.osu.edu/reps/