The equivariant cohomology of weighted flag orbifolds

Abstract

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

arXiv comment21 pages, substantially revised section 5 after referee's comments, accepted at Math. Z