Skip to Main Content

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.


Equivalence of categories between coefficient systems and systems of idempotents
HTML articles powered by AMS MathViewer

by Thomas Lanard
Represent. Theory 25 (2021), 422-439
Published electronically: June 2, 2021


The consistent systems of idempotents of Meyer and Solleveld allow to construct Serre subcategories of $\operatorname {Rep}_R(G)$, the category of smooth representations of a $p$-adic group $G$ with coefficients in $R$. In particular, they were used to construct level 0 decompositions when $R=\overline {\mathbb {Z}}_{\ell }$, $\ell \neq p$, by Dat for $GL_{n}$ and the author for a more general group. Wang proved in the case of $GL_{n}$ that the subcategory associated with a system of idempotents is equivalent to a category of coefficient systems on the Bruhat-Tits building. This result was used by Dat to prove an equivalence between an arbitrary level zero block of $GL_{n}$ and a unipotent block of another group. In this paper, we generalize Wang’s equivalence of category to a connected reductive group on a non-archimedean local field.
Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2020): 22E50, 20E42
  • Retrieve articles in all journals with MSC (2020): 22E50, 20E42
Bibliographic Information
  • Thomas Lanard
  • Affiliation: Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
  • MR Author ID: 1288084
  • Email:
  • Received by editor(s): August 4, 2020
  • Received by editor(s) in revised form: January 14, 2021, and February 8, 2021
  • Published electronically: June 2, 2021
  • © Copyright 2021 American Mathematical Society
  • Journal: Represent. Theory 25 (2021), 422-439
  • MSC (2020): Primary 22E50; Secondary 20E42
  • DOI:
  • MathSciNet review: 4273167