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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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Unipotent representations as a categorical centre
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by G. Lusztig PDF
Represent. Theory 19 (2015), 211-235 Request permission


Let $G(F_q)$ be the group of rational points of a split connected reductive group $G$ over the finite field $F_q$. In this paper we show that the category of representations of $G(F_q)$ which are finite direct sums of unipotent representations in a fixed two-sided cell is equivalent to the centre of a certain monoidal category of sheaves on the flag manifold of $G\times G$. We also consider a version of this for nonsplit groups.
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Additional Information
  • G. Lusztig
  • Affiliation: Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139
  • MR Author ID: 117100
  • Email:
  • Received by editor(s): December 5, 2014
  • Received by editor(s) in revised form: August 26, 2015
  • Published electronically: October 28, 2015
  • Additional Notes: Supported in part by National Science Foundation grant 1303060.
  • © Copyright 2015 American Mathematical Society
  • Journal: Represent. Theory 19 (2015), 211-235
  • MSC (2010): Primary 20G99
  • DOI:
  • MathSciNet review: 3416310