An Integration Formula of Shahidi
نویسنده
چکیده
To analyze the standard intertwining operators for induced representations of a reductive group, one is naturally led to study certain integrals over the corresponding unipotent radical N . A Levi component M acts on N by the adjoint action, and so we may decompose the integral according to the Ad(M)-orbits. We treat unitary and classical cases in which M is the product G×H of two groups related by the norm correspondence of Kottwitz-Shelstad. The result is a Weyl integration-type formula for the integral over N . Our expression for the functional illuminates the interaction between the matched conjugacy classes of G and H. This is part of an ongoing project to relate the poles of these operators to twisted endoscopy.
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