The equivariant cohomology of weighted flag orbifolds

We describe the torus-equivariant cohomology of weighted partial flag orbifolds w Sigma of type A. We establish counterparts of several results known for the partial flag variety that collectively constitute what we refer to as "Schubert Calculus on w Sigma ". For the weighed Schubert classes in w Sigma, we give the Chevalley's formula. In addition, we define the weighted analogue of double Schubert polynomials and give the corresponding Chevalley-Monk's formula.