Unipotent representations as a categorical centre

Lusztig, G.

doi:10.1090/ert/468

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

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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