Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165

 
 

 

Jordan decompositions of cocenters of reductive $ p$-adic groups


Authors: Xuhua He and Ju-Lee Kim
Journal: Represent. Theory 23 (2019), 294-324
MSC (2010): Primary 22E50; Secondary 11F70
DOI: https://doi.org/10.1090/ert/528
Published electronically: September 16, 2019
MathSciNet review: 4007169
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Cocenters of Hecke algebras $ \mathcal {H}$ play an important role in studying mod $ \ell $ or $ \mathbb{C}$ harmonic analysis on connected $ p$-adic reductive groups. On the other hand, the depth $ r$ Hecke algebra $ \mathcal {H}_{r^+}$ is well suited to study depth $ r$ smooth representations. In this paper, we study depth $ r$ rigid cocenters $ \overline {\mathcal {H}}^\mathrm {rig}_{r^+}$ of a connected reductive $ p$-adic group over rings of characteristic zero or $ \ell \neq p$. More precisely, under some mild hypotheses, we establish a Jordan decomposition of the depth $ r$ rigid cocenter, hence find an explicit basis of $ \overline {\mathcal {H}}^\mathrm {rig}_{r^+}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 22E50, 11F70

Retrieve articles in all journals with MSC (2010): 22E50, 11F70


Additional Information

Xuhua He
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Address at time of publication: The Institute of Mathematical Sciences and Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong.
Email: xuhuahe@math.cuhk.edu.hk

Ju-Lee Kim
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge Massachusetts 02139
Email: juleekim@mit.edu

DOI: https://doi.org/10.1090/ert/528
Received by editor(s): October 17, 2017
Received by editor(s) in revised form: October 30, 2018
Published electronically: September 16, 2019
Additional Notes: The first author was partially supported by NSF DMS-1463852 and DMS-1128155 (from IAS)
Article copyright: © Copyright 2019 American Mathematical Society