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Representation Theory

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Unipotent representations as a categorical centre

Author: G. Lusztig
Journal: Represent. Theory 19 (2015), 211-235
MSC (2010): Primary 20G99
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
MR Author ID: 117100

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