Cotangent Schubert Calculus in Grassmannians

Abstract

We find formulas for the Segre-MacPherson classes of Schubert cells in T-equivariant cohomology and the motivic Segre classes of Schubert cells in T-equivariant K-theory. In doing so we look at the pushforward of the projection map from the Bott-Samelson (Kempf-Laksov) desingularization to the Grassmannian. We find that the Segre-MacPherson classes are stable under pullbacks of maps embedding a Grassmannian into a bigger Grassmannian. We also express these formulas using certain Demazure-Lusztig operators that have previously been used to study these classes.