The Bernstein Center of the category of smooth W(k)[GLn(F)]-modules
File(s)
Author(s)
Helm, D
Type
Journal Article
Abstract
We consider the category of smooth -modules, where is a -adic field and is an algebraically closed field of characteristic different from . We describe a factorization of this category into blocks, and show that the center of each such block is a reduced, -torsion free, finite type -algebra. Moreover, the -points of the center of a such a block are in bijection with the possible ‘supercuspidal supports’ of the smooth -modules that lie in the block. Finally, we describe a large explicit subalgebra of the center of each block and give a description of the action of this algebra on the simple objects of the block, in terms of the description of the classical ‘characteristic zero’ Bernstein center of Bernstein and Deligne [Le ‘centre’ de Bernstein, in Representations des groups redutifs sur un corps local, Traveaux en cours (ed. P. Deligne) (Hermann, Paris), 1–32].
Date Issued
2016-06-07
Date Acceptance
2016-04-21
Citation
Forum of Mathematics, Sigma, 2016, 4
ISSN
2050-5094
Publisher
Cambridge University Press (CUP)
Journal / Book Title
Forum of Mathematics, Sigma
Volume
4
Copyright Statement
© The Author 2016. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence
(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the
original work is properly cited.
(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the
original work is properly cited.
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000377239900002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
EP/M029719/1
Subjects
Science & Technology
Physical Sciences
Mathematics
P-ADIC GROUPS
LANGLANDS CORRESPONDENCE
REPRESENTATIONS
INDUCTION
GL(N)
Publication Status
Published
Article Number
ARTN e11
Date Publish Online
2016-06-07