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REPRESENTATIONS OF REDUCTIVE p-ADIC GROUPS: LOCALIZATION OF HECKE ALGEBRAS AND APPLICATIONS

Published online by Cambridge University Press:  08 April 2017

COLIN J. BUSHNELL
Affiliation:
Department of Mathematics, King's College, Strand, London WC2R 2LS; bushnell@mth.kcl.ac.uk
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Abstract

Let F be a non-Archimedean local field and G be the group of F-points of a connected reductive group defined over F. Let M be an F-Levi subgroup of G and P = MN be a parabolic subgroup with Levi decomposition P = MN. Jacquet, or truncated, restriction gives a functor from the category of smooth representations of G to that of M. The main result describes this functor in terms of homomorphisms and localizations of Hecke algebras attached to certain compact open subgroups of G and M. This leads to new and straightforward proofs of some fundamental results. The first computes the smooth dual of a Jacquet module of a smooth representation of G, generalizing the corresponding result for admissible representations due to Harish-Chandra and Casselman. The second identifies the co-adjoint of the Jacquet functor relative to P as the induction functor relative to the M-opposite of P, an unpublished result of J.-N. Bernstein.

Type
Notes and Papers
Copyright
The London Mathematical Society 2001

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REPRESENTATIONS OF REDUCTIVE p-ADIC GROUPS: LOCALIZATION OF HECKE ALGEBRAS AND APPLICATIONS
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