Modular generalized Springer correspondence I: the general linear group

Abstract

We define a generalized Springer correspondence for the group GL($n$) over any field. We also determine the cuspidal pairs, and compute the correspondence explicitly. Finally we define a stratification of the category of equivariant perverse sheaves on the nilpotent cone of GL($n$) satisfying the ‘recollement’ properties, and with subquotients equivalent to categories of representations of a product of symmetric groups.