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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Jordan decompositions of cocenters of reductive $p$-adic groups
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by Xuhua He and Ju-Lee Kim PDF
Represent. Theory 23 (2019), 294-324 Request permission


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 $\overline {\mathcal {H}}^\mathrm {rig}_{r^+}$.
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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.
  • MR Author ID: 733194
  • Email:
  • Ju-Lee Kim
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge Massachusetts 02139
  • MR Author ID: 653104
  • Email:
  • 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)
  • © Copyright 2019 American Mathematical Society
  • Journal: Represent. Theory 23 (2019), 294-324
  • MSC (2010): Primary 22E50; Secondary 11F70
  • DOI:
  • MathSciNet review: 4007169