A parametrization of unipotent representations

Abstract

We define a map from the unipotent representations of a split semisimple group over a finite field to (essentially) the set of pairs of left cells representations of the Weyl group in the same two-sided cell. We use this map to parametrize the unipotent representations.

44 pages. This paper superseds arxiv:2011.05362 which is withdrawn. Some corrections are made