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.

v1: 27 pages; v2: 29 pages, minor corrections; v3: 29 pages, final version, to appear in JEMS