Unipotent representations as a categorical centre

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.

26 pages. This version considers also nonsplit groups. arXiv admin note: text overlap with arXiv:1308.1082

References in corpus (2)

• Restriction of a character sheaf to conjugacy classes
• Truncated convolution of character sheaves

Cited by in corpus (1)

• Nonsplit Hecke algebras and perverse sheaves