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