Springer basic sets and modular Springer correspondence for classical types

Abstract

We define the notion of basic set data for finite groups (building on the notion of basic set, but including an order on the irreducible characters as part of the structure), and we prove that the Springer correspondence provides basic set data for Weyl groups. Then we use this to determine explicitly the modular Springer correspondence for classical types (for representations in odd characteristic). In order to do so, we compare the order on bipartitions introduced by Dipper and James with the order induced by the Springer correspondence.Comment: 31 page