Spherical representations and the Satake isomorphism
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چکیده
Last updated: December 10, 2013. Topics: Motivation for the study of spherical representations; Satake isomorphism stated for the general case of a connected reductive group (taking Bruhat-Tits theory as a black box); interpretation (spherical principal series, Satake parameter, representations of dual reductive group); Satake made more explicit for the split case (key calculation); idea of proof in the general case (mostly punted to Cartier’s Corvallis article [Car79]).
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