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Unipotent representations as a categorical centre


Author: G. Lusztig
Journal: Represent. Theory 19 (2015), 211-235
MSC (2010): Primary 20G99
DOI: https://doi.org/10.1090/ert/468
Published electronically: October 28, 2015
MathSciNet review: 3416310
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Abstract: 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
Email: gyuri@math.mit.edu

DOI: https://doi.org/10.1090/ert/468
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.
Article copyright: © Copyright 2015 American Mathematical Society