Truncated convolution of character sheaves

Abstract

Let G be a reductive, connected algebraic group over an algebraic closure of a finite field. We define a tensor structure on the category of perverse sheaves on G which are direct sums of unipotent character sheaves in a fixed two-sided cell; we show that this is equivalent to the centre with a known monoidal abelian category (a categorification of the J-ring associated to the same two-sided cell). ©2015