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COCENTERS OF $p$-ADIC GROUPS, I: NEWTON DECOMPOSITION

Part of: Representation theory of groups Lie groups

Published online by Cambridge University Press:  28 March 2018

XUHUA HE
XUHUA HE*
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA Institute for Advanced Study, Princeton, NJ 08540, USA; xuhuahe@math.umd.edu

Abstract

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In this paper, we introduce the Newton decomposition on a connected reductive $p$-adic group $G$. Based on it we give a nice decomposition of the cocenter of its Hecke algebra. Here we consider both the ordinary cocenter associated to the usual conjugation action on $G$ and the twisted cocenter arising from the theory of twisted endoscopy. We give Iwahori–Matsumoto type generators on the Newton components of the cocenter. Based on it, we prove a generalization of Howe’s conjecture on the restriction of (both ordinary and twisted) invariant distributions. Finally we give an explicit description of the structure of the rigid cocenter.

MSC classification

Primary: 22E50: Representations of Lie and linear algebraic groups over local fields
Secondary: 20C08: Hecke algebras and their representations
Type
Research Article
Information
Forum of Mathematics, Pi , Volume 6 , 2018 , e2
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Creative Commons
Creative Common License - CCCreative Common License - BY
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.
Copyright
© The Author 2018

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