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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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Cocenters and representations of pro-$p$ Hecke algebras
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by Xuhua He and Sian Nie PDF
Represent. Theory 21 (2017), 82-105 Request permission


In this paper, we study the relation between the cocenter $\overline {{\tilde {\mathcal H}}}$ and the representations of an affine pro-$p$ Hecke algebra ${\tilde {\mathcal H}}={\tilde {\mathcal H}}(0, -)$. As a consequence, we obtain a new criterion on supersingular representations: a (virtual) representation of ${\tilde {\mathcal H}}$ is supersingular if and only if its character vanishes on the non-supersingular part of the cocenter $\overline {\tilde {\mathcal H}}$.
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Additional Information
  • Xuhua He
  • Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
  • MR Author ID: 733194
  • Email:
  • Sian Nie
  • Affiliation: Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, People’s Republic of China
  • Email:
  • Received by editor(s): May 11, 2016
  • Received by editor(s) in revised form: October 10, 2016, December 1, 2016, February 26, 2017, and May 10, 2017
  • Published electronically: June 23, 2017
  • Additional Notes: The first author was partially supported by NSF DMS-1463852. The second author was partially supported by NSFC (No. 11501547 and No. 11621061.) and by the Key Research Program of Frontier Sciences, CAS, Grant No. QYZDB-SSW-SYS007.
  • © Copyright 2017 American Mathematical Society
  • Journal: Represent. Theory 21 (2017), 82-105
  • MSC (2010): Primary 20C08, 20C20, 22E50
  • DOI:
  • MathSciNet review: 3665615