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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Jordan decompositions of cocenters of reductive $p$-adic groups
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by Xuhua He and Ju-Lee Kim
Represent. Theory 23 (2019), 294-324
Published electronically: September 16, 2019


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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Bibliographic 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