Seminar
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Location: | SLMath: Eisenbud Auditorium |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
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Secondary Mathematics Subject Classification
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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.
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