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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 16:17:12 +0000A formula for the geometric Jacquet functor and its character sheaf analogue
https://resolver.caltech.edu/CaltechAUTHORS:20170707-075734325
Authors: {'items': [{'id': 'Chen-Tsao-Hsien', 'name': {'family': 'Chen', 'given': 'Tsao-Hsien'}}, {'id': 'Yom-Din-A', 'name': {'family': 'Yom Din', 'given': 'Alexander'}}]}
Year: 2017
DOI: 10.1007/s00039-017-0413-z
Let (G,K) be a symmetric pair over the complex numbers, and let X=K∖GX=K∖G be the corresponding symmetric space. In this paper we study a nearby cycles functor associated to a degeneration of X to MN∖GMN∖G , which we call the "wonderful degeneration". We show that on the category of character sheaves on X, this functor is isomorphic to a composition of two averaging functors (a parallel result, on the level of functions in the p-adic setting, was obtained in [BK,SV]). As an application, we obtain a formula for the geometric Jacquet functor of [ENV] and use this formula to give a geometric proof of the celebrated Casselman's submodule theorem and establish a second adjointness theorem for Harish-Chandra modules.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dr0c5-58v38