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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.


Hecke modules and supersingular representations of U(2,1)
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by Karol Kozioł and Peng Xu
Represent. Theory 19 (2015), 56-93
Published electronically: March 16, 2015


Let $F$ be a nonarchimedean local field of odd residual characteristic $p$. We classify finite-dimensional simple right modules for the pro-$p$-Iwahori-Hecke algebra $\mathcal {H}_C(G,I(1))$, where $G$ is the unramified unitary group $\textrm {U}(2,1)(E/F)$ in three variables. Using this description when $C = \overline {\mathbb {F}}_p$, we define supersingular Hecke modules and show that the functor of $I(1)$-invariants induces a bijection between irreducible nonsupersingular mod-$p$ representations of $G$ and nonsupersingular simple right $\mathcal {H}_C(G,I(1))$-modules. We then use an argument of Paškūnas to construct supersingular representations of $G$.
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Bibliographic Information
  • Karol Kozioł
  • Affiliation: Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada M5S 2E4
  • MR Author ID: 1099660
  • Email:
  • Peng Xu
  • Affiliation: Mathematics Institute, University of Warwick, Zeeman Building, Coventry CV4 7AL, United Kingdom
  • MR Author ID: 1099916
  • Email:
  • Received by editor(s): September 29, 2014
  • Received by editor(s) in revised form: November 25, 2014
  • Published electronically: March 16, 2015
  • Additional Notes: The first author was supported by NSF Grant DMS-0739400.
    The second author was supported by EPSRC Grant EP/H00534X/1.
  • © Copyright 2015 American Mathematical Society
  • Journal: Represent. Theory 19 (2015), 56-93
  • MSC (2010): Primary 22E50, 20C08, 11F70, 20C20
  • DOI:
  • MathSciNet review: 3321473