The equivariant cohomology of weighted flag orbifolds

We describe the torus-equivariant cohomology of weighted partial flag orbifolds $\mathrm{w}\mathrm{\Sigma }$ 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 $\mathrm{w}\mathrm{\Sigma }$’'. For the weighed Schubert classes in $\mathrm{w}\mathrm{\Sigma }$, 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.