We compute the Chern-Schwartz-MacPherson classes of Schubert varieties in flag manifolds. These classes are obtained by constructing a representation of the Weil group, by means of certain Demazure-Lusztig type operators. The construction extends to the equivariant setting. Based on explicit computations in low dimension, we conjecture that these classes are Schubert-positive; the analogous conjecture for Schubert varieties of Grassmannians was recently proven by June Huh.

Coauthor: Leonardo Mihalcea