Formality and Lusztig's generalized Springer correspondence

We prove a derived equivalence between each block of the derived category of sheaves on the nilpotent cone and the category of differential graded modules over a degeneration of Lusztig’s graded Hecke algebra. Along the way, we construct and study a mixed version of the geometric category. This work can be viewed as giving a derived version of the generalized Springer correspondence.