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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.


L’involution de Zelevinski modulo $\ell$
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by Alberto Mínguez and Vincent Sécherre
Represent. Theory 19 (2015), 236-262
Published electronically: October 29, 2015


Let $\mathrm {F}$ be a non-Archimedean locally compact field with residual characteristic $p$, let $\mathrm {G}$ be an inner form of $\mathrm {GL}_n(\mathrm {F})$, $n\geqslant 1$ and let $\mathrm {R}$ be an algebraically closed field of characteristic different from $p$. When $\mathrm {R}$ has characteristic $\ell >0$, the image of an irreducible smooth $\mathrm {R}$-representation $\pi$ of $\mathrm {G}$ by the Aubert involution need not be irreducible. We prove that this image (in the Grothendieck group of $\mathrm {G}$) contains a unique irreducible term $\pi ^\star$ with the same cuspidal support as $\pi$. This defines an involution $\pi \mapsto \pi ^\star$ on the set of isomorphism classes of irreducible $\mathrm {R}$-representations of $\mathrm {G}$, that coincides with the Zelevinski involution when $\mathrm {R}$ is the field of complex numbers. The method we use also works for $\mathrm {F}$ a finite field of characteristic $p$, in which case we get a similar result.
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Bibliographic Information
  • Alberto Mínguez
  • Affiliation: Institut de Mathématiques de Jussieu, Université Paris 6, 4 place Jussieu, 75005, Paris, France
  • Address at time of publication: Institut de Mathématiques de Jussieu – Paris Rive Gauche, Université Pierre et Marie Curie, 4 place Jussieu, 75005, Paris, France.
  • Email:
  • Vincent Sécherre
  • Affiliation: Université de Versailles Saint-Quentin-en-Yvelines, Laboratoire de Mathématiques de Versailles, 45 avenue des Etats-Unis, 78035 Versailles cedex, France
  • Address at time of publication: Laboratoire de Mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay, 78035 Versailles, France
  • MR Author ID: 741262
  • Email:
  • Received by editor(s): December 17, 2014
  • Received by editor(s) in revised form: August 28, 2015
  • Published electronically: October 29, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Represent. Theory 19 (2015), 236-262
  • MSC (2010): Primary 22E50, 20G40
  • DOI:
  • MathSciNet review: 3416734