Unipotent representations as a categorical centre
Representation Theory
2014-02-18 v2
Abstract
Let G(F_q) be the group of rational points of a split connected reductive group G defined 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 product of two copies of the flag manifold of G. We also consider a version of this for nonsplit groups.
Cite
@article{arxiv.1401.2889,
title = {Unipotent representations as a categorical centre},
author = {G. Lusztig},
journal= {arXiv preprint arXiv:1401.2889},
year = {2014}
}
Comments
26 pages. This version considers also nonsplit groups. arXiv admin note: text overlap with arXiv:1308.1082