The aim of this paper is to work out a concrete example as well as to provide the general pattern of applications of Koszul duality to repre- sentation theory. The paper consists of three parts… Expand

Let D : Db(x, ~ ) be the usual derived category of ~-sheaves on a certain scheme X, and M = M{X)c D be the category of perverse sheaves for middle perversity. Now consider the derived category Db(M)… Expand

We consider the interplay of infinite-dimensional Lie algebras of Virasoro type and moduli spaces of curves, suggested by string theory. We will see that the infinitesimal geometry of determinant… Expand

The aim of this note [0] is to give a short, self-contained account of the vanishing cycle constructions of perverse sheaves; e.g., for the needs of [1]. It differs somewhat from the alternative… Expand

We discuss tilting objects in categories of perverse sheaves smooth along some stratification. In case of the Schubert stratification we show that the Radon transform interchanges tilting,… Expand